Sample Splitting Research Articles

A Unified Framework for Covariate Adjustment Under Stratified Randomisation

ABSTRACTRandomisation, as a key technique in clinical trials, can eliminate sources of bias and produce comparable treatment groups. In randomised experiments, the treatment effect is a parameter of general interest. Researchers have explored the validity of using linear models to estimate the treatment effect and perform covariate adjustment and thus improve the estimation efficiency. However, the relationship between covariates and outcomes is not necessarily linear, and is often intricate. Advances in statistical theory and related computer technology allow us to use nonparametric and machine learning methods to better estimate the relationship between covariates and outcomes and thus obtain further efficiency gains. However, theoretical studies on how to draw valid inferences when using nonparametric and machine learning methods under stratified randomisation are yet to be conducted. In this paper, we discuss a unified framework for covariate adjustment and corresponding statistical inference under stratified randomisation and present a detailed proof of the validity of using local linear kernel‐weighted least squares regression for covariate adjustment in treatment effect estimators as a special case. In the case of high‐dimensional data, we additionally propose an algorithm for statistical inference using machine learning methods under stratified randomisation, which makes use of sample splitting to alleviate the requirements on the asymptotic properties of machine learning methods. Finally, we compare the performances of treatment effect estimators using different machine learning methods by considering various data generation scenarios, to guide practical research.

Multiplexed chromatin immunoprecipitation sequencing for quantitative study of histone modifications and chromatin factors.

ChIP-seq is a widely used technique for studying histone post-translational modifications and DNA-binding proteins. DNA fragments associated with a specific protein or histone modification epitope are captured by using antibodies, sequenced and mapped to a reference genome. Albeit versatile and popular, performing many parallel ChIP-seq experiments to compare different conditions, replicates and epitopes is laborious, is prone to experimental variation and does not allow quantitative comparisons unless adequate spike-in chromatin is included. We present a detailed protocol for performing and analyzing a multiplexed quantitative chromatin immunoprecipitation-sequencing experiment (MINUTE-ChIP), in which multiple samples are profiled against multiple epitopes in a single workflow. Multiplexing not only dramatically increases the throughput of ChIP-seq experiments (e.g., profiling 12 samples against multiple histone modifications or DNA-binding proteins in a single experiment), but also enables accurate quantitative comparisons. The protocol consists of four parts: sample preparation (i.e., lysis, chromatin fragmentation and barcoding of native or formaldehyde-fixed material), pooling and splitting of the barcoded chromatin into parallel immunoprecipitation reactions, preparation of next-generation sequencing libraries from input and immunoprecipitated DNA and data analysis using our dedicated analysis pipeline. This pipeline autonomously generates quantitatively scaled ChIP-seq tracks for downstream analysis and visualization, alongside necessary quality control indicators. The entire workflow requires basic knowledge in molecular biology and bioinformatics and can be completed in 1 week. MINUTE-ChIP empowers biologists to perform every ChIP-seq experiment with an appropriate number of replicates and control conditions, delivering more statistically robust, exquisitely quantitative and biologically meaningful results.

Corrected generalized cross-validation for finite ensembles of penalized estimators

Abstract Generalized cross-validation (GCV) is a widely used method for estimating the squared out-of-sample prediction risk that employs scalar degrees of freedom adjustment (in a multiplicative sense) to the squared training error. In this paper, we examine the consistency of GCV for estimating the prediction risk of arbitrary ensembles of penalized least-squares estimators. We show that GCV is inconsistent for any finite ensemble of size greater than one. Towards repairing this shortcoming, we identify a correction that involves an additional scalar correction (in an additive sense) based on degrees of freedom adjusted training errors from each ensemble component. The proposed estimator (termed CGCV) maintains the computational advantages of GCV and requires neither sample splitting, model refitting, or out-of-bag risk estimation. The estimator stems from a finer inspection of the ensemble risk decomposition and two intermediate risk estimators for the components in this decomposition. We provide a non-asymptotic analysis of the CGCV and the two intermediate risk estimators for ensembles of convex penalized estimators under Gaussian features and a linear response model. Furthermore, in the special case of ridge regression, we extend the analysis to general feature and response distributions using random matrix theory, which establishes model-free uniform consistency of CGCV.

Debiased lasso after sample splitting for estimation and inference in high‐dimensional generalized linear models

Debiased lasso after sample splitting for estimation and inference in high‐dimensional generalized linear models

Printed and Laser Induced Graphene Electrochemical Biosensors for Rapid Environmental and Biomedical Monitoring

This presentation will demonstrate how low-cost printed and flexible graphene circuits can overcome the challenges associated with conventional electrical circuits to open the door to a highly sensitive monitoring of biochemical threats and toxins including nerve agents/pesticides. The use of inkjet and aerosol printing; spin coating; and laser writing (i.e., laser induced graphene) can be used to create such circuits with high resolution (line widths as low as 20 µm). Moreover, the use of rapid-pulse laser annealing of the printed graphene and/or salt porogens added into graphene inks before printing can be used to further improve the electrical conductivity (< 10 ohms/sq.) and electroactive surface area (nano/micro structuring) of the graphene circuits as well as be used to tune the surface of the printed graphene from one that is hydrophilic (water contact angle (WCA) = 48°) to one that is superhydrophobic (WCA = 158°). More recently we demonstrate how graphene synthesis, patterning and surface wettability can all be controlled through a laser induced graphene (LIG) process that creates a high surface area graphene surface directly from polyimide. Such LIG circumvents the need to create solution-phase graphene inks for printing. These printing and laser fabrication techniques are also amenable for use on flexible and chemically/thermally sensitive surfaces including polymers and paper.Moreover, the laser etched printed graphene and LIG exhibits an inherent 3D morphology that significantly increases the electrode electroactive surface over traditional 2D planar graphene electrodes. This large increase in surface area significantly improves the loading of enzyme onto the electrode surface and subsequently increases the heterogenous charge transport during catalytic pesticide sensing. Such ion sensors displayed near-Nernstian sensitivities, wide sensing ranges over four orders of magnitude extending from the 10–2 M down to detection limits in the 10–6 M range or for fertilizer ions (nitrate, ammonium, potassium, calcium, and magnesium) reaching down to detection limits less than 1 ppm in some cases in soil and water samples. The pesticide sensing capability of the sensor is able to reach an extremely low picomolar detect limit for organophosphates (paraoxon) and to the nanomolar regime for neonicotinoids in surface waters. We also demonstrate how this flexible LIG electrodes can be coupled with polymeric microfluidics and adhered to the body for continuous monitoring of lactate, glucose, and sodium in the sweat. Finally, we demonstrate how such surface wettability patterning of the printed graphene and LIG itself through laser etching can be used to make hydrophilic LIG tracks surrounded by near superhydrophic sidewalls for open microfluidic fluid transport without the need for polymeric microfluidics. Such open microfluidic tracks enable the splitting and transport of fluid samples to distinct electrochemical sensors for multiplexed biosensing of both fertilizer ion and pesticide monitoring from water samples and assist in harvesting sprayed pesticides in the field. Figure 1

Estimating Brazilian Amazon Canopy Height Using Landsat Reflectance Products in a Random Forest Model with Lidar as Reference Data

Landsat data have been used to derive forest canopy structure, height, and volume using machine learning models, i.e., giving computers the ability to learn from data and make decisions and predictions without being explicitly programmed, with training data provided by ground measurement or airborne lidar. This study explored the potential use of Landsat reflectance and airborne lidar data as training data to estimate canopy heights in the Brazilian Amazon forest and examined the impacts of Landsat reflectance products at different process levels and sample spatial autocorrelation on random forest modeling. Specifically, this study assessed the accuracy of canopy height predictions from random forest regression models impacted by three different Landsat 8 reflectance product inputs (i.e., USGS level 1 top of atmosphere reflectance, USGS level 2 surface reflectance, and NASA nadir bidirectional reflectance distribution function (BRDF) adjusted reflectance (NBAR)), sample sizes, training/test split strategies, and geographic coordinates. In the establishment of random forest regression models, the dependent variable (i.e., the response variable) was the dominant canopy heights at a 90 m resolution derived from airborne lidar data, while the independent variables (i.e., the predictor variables) were the temporal metrics extracted from each Landsat reflectance product. The results indicated that the choice of Landsat reflectance products had an impact on model accuracy, with NBAR data yielding more trustful results than the other products despite having higher RMSE values. Training and test split strategy also affected the derived model accuracy metrics, with the random sample split (randomly distributed training and test samples) showing inflated accuracy compared to the spatial split (training and test samples spatially set apart). Such inflation was induced by the spatial autocorrelation that existed between training and test data in the random split. The inclusion of geographic coordinates as independent variables improved model accuracy in the random split strategy but not in the spatial split, where training and test samples had different geographic coordinate ranges. The study highlighted the importance of data processing levels and the training and test split methods in random forest modeling of canopy height.

METODE RANDOM FOREST UNTUK MEMUDAHKAN KLASIFIKASI DIAGNOSIS PENYAKIT MENTAL

Mental health is important in the development of every individual. A bad mentality can prevent a person from developing, making a person easily stressed, hopeless, and even attempt suicide and commit crimes. Currently there are quite a lot of case related to mental health which are caused by many factors such as economic, social and medical. Reflecting on this fact, there is a need for rapid mental health detection so that immediate intervention can be carried out. This needs to be done so that the patient's condition can improve. This research focuses on diagnosing mental illness by utilizing machine learning. The method used is random forest which in several studies has been proven to produce good accuracy. Random forest performs machine learning on the attributes contained in the dataset combined with K-Fold Cross Validation so that each patient can be evaluated. Next, a tuning process is also carried out to test the parameters contained in the method. After the tuning process was carried out, the best parameters obtained were n-estimator of 30, maximum depth of 4, minimum sample leaf of 2, and minimum sample split of 10. From the combination of these parameters, accuracy is 90.83%, recall is 90.83 %, and precision of 93.25%.

High-dimensional causal mediation analysis by partial sum statistic and sample splitting strategy in imaging genetics application.

Causal mediation analysis provides a systematic approach to explore the causal role of one or more mediators in the association between exposure and outcome. In omics or imaging data analysis, mediators are often high-dimensional, which brings new statistical challenges. Existing methods either violate causal assumptions or fail in interpretable variable selection. Additionally, mediators are often highly correlated, presenting difficulties in selecting and prioritizing top mediators. To address these issues, we develop a framework using Partial Sum Statistic and Sample Splitting Strategy, namely PS5, for high-dimensional causal mediation analysis. The method provides a powerful global mediation test satisfying causal assumptions, followed by an algorithm to select and prioritize active mediators with quantification of individual mediation contributions. We demonstrate its accurate type I error control, superior statistical power, reduced bias in mediation effect estimation, and accurate mediator selection using extensive simulations of varying levels of effect size, signal sparsity, and mediator correlations. Finally, we apply PS5 to an imaging genetics dataset of chronic obstructive pulmonary disease (COPD) patients ( N =8,897) in the COPDGene study to examine the causal mediation role of lung images ( p =5,810) in the associations between polygenic risk score and lung function and between smoking exposure and lung function, respectively. Both causal mediation analyses successfully estimate the global indirect effect and detect mediating image regions. Collectively, we find a region in the lower lobe of the right lung with a strong and concordant mediation effect for both genetic and environmental exposures. This suggests that targeted treatment toward this region might mitigate the severity of COPD due to genetic and smoking effects.

Generalized Data Thinning Using Sufficient Statistics

Our goal is to develop a general strategy to decompose a random variable X into multiple independent random variables, without sacrificing any information about unknown parameters. A recent paper showed that for some well-known natural exponential families, X can be thinned into independent random variables X ( 1 ) , … , X ( K ) , such that X = ∑ k = 1 K X ( k ) . These independent random variables can then be used for various model validation and inference tasks, including in contexts where traditional sample splitting fails. In this article, we generalize their procedure by relaxing this summation requirement and simply asking that some known function of the independent random variables exactly reconstruct X. This generalization of the procedure serves two purposes. First, it greatly expands the families of distributions for which thinning can be performed. Second, it unifies sample splitting and data thinning, which on the surface seem to be very different, as applications of the same principle. This shared principle is sufficiency. We use this insight to perform generalized thinning operations for a diverse set of families. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Clinical Predictors of Postmortem Amyloid and Nonamyloid Cerebral Small Vessel Disease in Middle-Aged to Older Adults.

Sporadic cerebral small vessel disease (CSVD) is a class of important pathologic processes known to affect the aging brain and to contribute to cognitive impairment. We aimed to identify clinical risk factors associated with postmortem CSVD in middle-aged to older adults. We developed and tested risk models for their predictive accuracy of a pathologic diagnosis of nonamyloid CSVD and cerebral amyloid angiopathy (CAA) in a retrospective sample of 160 autopsied cases from the Edinburgh Brain Bank. Individuals aged 40 years and older covering the spectrum of healthy aging and common forms of dementia (i.e., highly-prevalent etiologies such as Alzheimer disease (AD), vascular cognitive impairment (VCI), and mixed dementia) were included. We performed binomial logistic regression models using sample splitting and cross-validation methods. Demographics, lifestyle habits, traditional vascular risk factors, chronic medical conditions, APOE4, and cognitive status were assessed as potential predictors. Forty percent of our sample had a clinical diagnosis of dementia (AD = 33, VCI = 26 and mixed = 5) while others were cognitively healthy (n = 96). The mean age at death was 73.8 (SD 14.1) years, and 40% were female. The presence of none-to-mild vs moderate-to-severe nonamyloid CSVD was predicted by our model with good accuracy (area under the curve [AUC] = 0.84, sensitivity [SEN] = 72%, specificity [SPE] = 95%), with the most significant clinical predictors being age, history of cerebrovascular events, and cognitive impairment. The presence of CAA pathology was also predicted with high accuracy (AUC = 0.86, SEN = 93%, SPE = 79%). Significant predictors included alcohol intake, history of cerebrovascular events, and cognitive impairment. In a subset of atypical dementias (n = 24), our models provided poor predictive performance for both nonamyloid CSVD (AUC = 0.50) and CAA (AUC = 0.43). CSVD pathology can be predicted with high accuracy based on clinical factors in patients within the spectrum of AD, VCI, and normal aging. Whether this prediction can be enhanced by the addition of fluid and neuroimaging biomarkers warrants additional study. Improving our understanding of clinical determinants of vascular brain health may lead to novel strategies in the prevention and treatment of vascular etiologies contributing to cognitive decline. This study provides Class II evidence that selected clinical factors accurately distinguish between middle-aged to older adults with and without cerebrovascular small vessel disease (amyloid and nonamyloid) pathology.

Efficient Nonparametric Estimation of Stochastic Policy Effects with Clustered Interference

Interference occurs when a unit’s treatment (or exposure) affects another unit’s outcome. In some settings, units may be grouped into clusters such that it is reasonable to assume that interference, if present, only occurs between individuals in the same cluster, that is, there is clustered interference. Various causal estimands have been proposed to quantify treatment effects under clustered interference from observational data, but these estimands either entail treatment policies lacking real-world relevance or are based on parametric propensity score models. Here, we propose new causal estimands based on modification of the propensity score distribution which may be more relevant in many contexts and are not based on parametric models. Nonparametric sample splitting estimators of the new estimands are constructed, which allow for flexible data-adaptive estimation of nuisance functions and are consistent, asymptotically normal, and efficient, converging at the usual parametric rate. Simulations show the finite sample performance of the proposed estimators. The proposed methods are applied to evaluate the effect of water, sanitation, and hygiene facilities on diarrhea among children in Senegal. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

A new portmanteau test for predictive regression models with possible embedded endogeneity

In the widely used predictive regression model, any possible serial correlation in innovations leads to estimation bias and statistical inference distortions. Hence, it is important to pretest the existence of such serial correlation. Nevertheless, in the presence of embedded endogeneity, which is a common problem in the predictive regression setting, traditional serial correlation tests such as Box–Pierce (BP) and Ljung–Box (LB) tests are found to perform poorly. Motivated by this, we develop a new portmanteau test in this article as a pretest for serial correlation in predictive regression under possible embedded endogeneity. This test is based on the sample splitting idea and the jackknife empirical likelihood method. The asymptotic distribution of the proposed test has been derived, and the Monte Carlo simulations confirm good finite sample performances. As an illustration, we apply our proposed test in pretesting the serial correlation in predictive regression, where financial variables are used to predict the excess return of S&amp;P 500.

Left atrial function in patients with rheumatic mitral stenosis: addressing prognostic insights beyond atrial fibrillation prediction.

Rheumatic mitral stenosis (MS) frequently leads to impaired left atrial (LA) function because of pressure overload, highlighting the underlying atrial pathology. Two-dimensional speckle tracking echocardiography (2D-STE) offers early detection of LA dysfunction, potentially improving risk assessment in patients with MS. This study aims to evaluate the predictive value of LA function assessed by 2D-STE for clinical outcomes in patients with MS. Between 2011 and 2021, patients with MS underwent LA function assessment using 2D-STE, with focus on the reservoir phase (LASr). Atrial fibrillation (AF) development constituted the primary outcome, with death or valve replacement as the secondary outcome. Conditional inference trees were employed for analysis, validated through sample splitting. The study included 493 patients with MS (mean valve area 1.1 ± 0.4 cm2, 84% female). At baseline, 166 patients (34%) had AF, with 62 patients (19%) developing AF during follow-up. LASr emerged as the primary predictor for new-onset AF, with a threshold of 17.9%. Over a mean 3.8-year follow-up, 125 patients (25%) underwent mitral valve replacement, and 32 patients (6.5%) died. A decision tree analysis identified key predictors such as age, LASr, severity of tricuspid regurgitation (TR), net atrioventricular compliance (C n), and early percutaneous mitral valvuloplasty, especially in patients aged ≤49 years, where LASr, with a threshold of 12.8%, significantly predicted adverse outcomes. LASr emerged as a significant predictor of cardiovascular events in this MS cohort, validated through a decision tree analysis. Patients were stratified into low- or high-risk categories for adverse outcomes, taking into account LASr, age, TR severity, and C n.

Development and validation of the Dermatology Social Comparison (DSC) Scale.

Social comparison, the process of evaluating one's characteristics in relation to others, influences individuals' self-perception and behavior. However, instruments are scarce for assessing social comparison in the medical setting. Our aim was to develop and validate a new scale for assessing social comparison. Seven statements were developed, encompassing the perceived normality of having rashes, the tendency to compare their situation with others, and the emotional response when seeing someone better or worse off than themselves. The instrument was piloted in 15 patients for readability and face validity, then prospectively validated using modern psychometric methods in 1,053 adult patients with eczema or psoriasis from three tertiary dermatological centers in Singapore. Of 1,053 adult patients, 802 (76.2%) had eczema, and 251 (23.8%) had psoriasis. Exploratory factor analysis (using a 70% sample split) showed a single factor model comprising three questions (Eigenvalue: 1.4). Confirmatory factor analysis with the remaining 30% of the sample confirmed an excellent model fit. Cronbach's alpha was 0.7, and inter-item correlations ranged from 0.42 to 0.46. In the Rasch analysis, item fit statistics and item characteristic curves showed appropriate discrimination between response options, although reliability was suboptimal with a person separation reliability of 0.63. Comprising 3 questions, the newly derived social comparison scale showed acceptable psychometrics as a measure of social comparison for clinical and research purposes in dermatology. Its brief nature likely results from its brevity and applicability to conditions beyond eczema and psoriasis, which warrants further investigation.

Model-Based Reinforcement Learning for Offline Zero-Sum Markov Games

This paper makes progress toward learning Nash equilibria in two-player, zero-sum Markov games from offline data. Despite a large number of prior works tackling this problem, the state-of-the-art results suffer from the curse of multiple agents in the sense that their sample complexity bounds scale linearly with the total number of joint actions. The current paper proposes a new model-based algorithm, which provably finds an approximate Nash equilibrium with a sample complexity that scales linearly with the total number of individual actions. This work also develops a matching minimax lower bound, demonstrating the minimax optimality of the proposed algorithm for a broad regime of interest. An appealing feature of the result lies in algorithmic simplicity, which reveals the unnecessity of sophisticated variance reduction and sample splitting in achieving sample optimality.

Assessing computational predictions of antimicrobial resistance phenotypes from microbial genomes.

The advent of rapid whole-genome sequencing has created new opportunities for computational prediction of antimicrobial resistance (AMR) phenotypes from genomic data. Both rule-based and machine learning (ML) approaches have been explored for this task, but systematic benchmarking is still needed. Here, we evaluated four state-of-the-art ML methods (Kover, PhenotypeSeeker, Seq2Geno2Pheno and Aytan-Aktug), an ML baseline and the rule-based ResFinder by training and testing each of them across 78 species-antibiotic datasets, using a rigorous benchmarking workflow that integrates three evaluation approaches, each paired with three distinct sample splitting methods. Our analysis revealed considerable variation in the performance across techniques and datasets. Whereas ML methods generally excelled for closely related strains, ResFinder excelled for handling divergent genomes. Overall, Kover most frequently ranked top among the ML approaches, followed by PhenotypeSeeker and Seq2Geno2Pheno. AMR phenotypes for antibiotic classes such as macrolides and sulfonamides were predicted with the highest accuracies. The quality of predictions varied substantially across species-antibiotic combinations, particularly for beta-lactams; across species, resistance phenotyping of the beta-lactams compound, aztreonam, amoxicillin/clavulanic acid, cefoxitin, ceftazidime and piperacillin/tazobactam, alongside tetracyclines demonstrated more variable performance than the other benchmarked antibiotics. By organism, Campylobacter jejuni and Enterococcus faecium phenotypes were more robustly predicted than those of Escherichia coli, Staphylococcus aureus, Salmonella enterica, Neisseria gonorrhoeae, Klebsiella pneumoniae, Pseudomonas aeruginosa, Acinetobacter baumannii, Streptococcus pneumoniae and Mycobacterium tuberculosis. In addition, our study provides software recommendations for each species-antibiotic combination. It furthermore highlights the need for optimization for robust clinical applications, particularly for strains that diverge substantially from those used for training.

Abstract 2291: Bravo automation of Agilent Avida targeted enrichment for high-throughput detection of genomic alteration and DNA methylation

Abstract Background: Current genomic and epigenomic profiling of cancer tissue DNA or cfDNA (cell-free DNA) in liquid biopsy relies upon separate, time- and sample-consuming technologies for somatic variant detection or methylation analysis. Here we describe workflow and performance of the Agilent Bravo automated liquid handling platform with the Agilent Avida targeted enrichment solution for next generation sequencing of somatic variants and methylation profiling. This solution can effectively analyze low-input tumor DNA or cfDNA samples. The Avida Duo workflow enables highly sensitive detection of single nucleotide variant (SNV), insertions and deletions (INDEL), copy number variation (CNV) and DNA methylation profiles from a single sample, without any sample splitting. Methods and Results: Panels, reagents, and automated workflows for Avida DNA, Avida Methyl, and Avida Duo Methyl (combined DNA &amp; methylation) kits were developed to accommodate up to 96 samples on the Bravo NGS workstation. The automated solution supports independent single-day workflows for somatic variants or methylation sample preparation. The Avida Duo analysis combines both workflows without sample splitting, streamlining the process and reducing sample consumption. Leveraging a focused cancer hotspot panel, we demonstrate excellent reproducibility and low allele frequency (SNV at sub 1%) variant detection in cfDNA samples and reference standards with as little as 10ng DNA input. We exhibit similar performance with a larger ~300 kb target region tumor profiling panel. Finally, we demonstrate DNA methylation detection in the standalone or combined (“Duo”) workflows across differentially methylated regions (DMRs) with a panel of ~3400 targets. Conclusions: Automation of the Avida targeted enrichment solution with the Bravo NGS workstation enables a sensitive, high-throughput, end-to-end analysis for detection of genomic alterations and DNA methylation changes from a single low-input cfDNA or tumor DNA sample. Citation Format: Ashraf Wahba, Tony Ho, Sarah Johns, Aswati Aravind, Heng Wang, Neelima V. Mehendale, Gilbert P. Amparo, Khine Win, Manuel Gomez, Grace Zhao, Douglas N. Roberts. Bravo automation of Agilent Avida targeted enrichment for high-throughput detection of genomic alteration and DNA methylation [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2024; Part 1 (Regular Abstracts); 2024 Apr 5-10; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2024;84(6_Suppl):Abstract nr 2291.

Foreign direct investment and inclusive finance: do financial markets and quality of institutions matter?

We examine the impact of foreign direct investment (FDI) on financial inclusion. To identify the causal effect of FDI on financial inclusion, we use plausibly exogenous source of variations in bilateral investment treaties (BITs) as a novel instrumental variable (IV) for net FDI inflows. Using annual data for a broad panel of 90 countries over the period 2004 to 2017, our results show that FDI improves financial inclusion for both “access to finance" and “use of financial services". This impact is more pronounced for relatively poor countries and developing countries compared to rich and developed countries. We also find that higher financial market development and quality institutions improve financial inclusion directly. Moreover, financial market development and institutional quality can serve as potential channels and moderating variables through which FDI affects financial inclusion. Our results are robust to various estimations and sample splitting and have important implications for policy on financial inclusion.

Inflation-Economic Growth Nexus in Nigeria: New Evidence on Threshold Effects

Purpose: The aim of this study is to analyze the influence of inflation on the economic growth of Nigeria from 1990 to 2021. Specifically, it aims to identify a threshold, if it exists, at which the impact of inflation on economic growth begins to shift.&#x0D; Methodology: To assess the inflation threshold and its impact on economic growth, this study employed a novel method, the endogenous sample-splitting and threshold model developed by Hansen (2000).&#x0D; Findings: The study reveals a non-linear relationship between inflation and economic growth in Nigeria, with a single inflation threshold of 12.88%. When inflation is below this threshold, it positively impacts economic growth, while exceeding it negatively impacts economic growth. Furthermore, higher trade openness negatively affects economic growth, and population growth positively impacts growth across all inflation regimes. Investments contribute to economic growth in the linear model, but their influence is statistically insignificant across the threshold regimes. Financial deepening impedes growth above the inflation threshold.&#x0D; Unique Contribution to Theory, Practice and Policy: The study expands upon the current body of research on estimating the inflation threshold for Nigeria using the Hansen (2000) sample splitting technique. To our knowledge, this is the first study that has adopted this technique to estimate inflation threshold for Nigeria. The Hansen (2000) threshold technique offers more flexibility in model specification. It allows for the estimation of parameters separately for different regimes, typically above and below the threshold. This flexibility can help in identifying distinct regimes, such as low and high inflation regimes, and capturing their unique characteristics. The research findings are crucial for shaping monetary policy in Nigeria, providing policymakers with valuable insights for establishing an inflation target that is in line with Nigeria's overarching goal of attaining sustained economic growth.

Towards Achieving the Sustainable Development Goals (SDGs): The Impact of Debts on Income Inequality in Africa

The Agenda for Sustainable Development provides a framework for the creation of a better and sustainable future for all. The Sustainable Development Goals (SDGs) focus on addressing global challenges, including income inequality. Among others, the SDGs also commit countries to work towards reducing income inequality and as such, lowering income inequality is one of the key issues in Africa. However, given the high levels of debt on the continent, reducing income inequality could be a challenge. Majority of the literature examines the link between debts and economic growth with little attention paid to the impact of debts on income inequality. Moreover, not much is known on whether the relationship between debt and income inequality is non–linear. This study therefore contributes to the existing research efforts by investigating the threshold effects of debts using data from 24 African countries by relying on the sample splitting and threshold estimation approach. The results reveal that, while debts generally dampen income inequality, unbridled debt accumulation above the estimated thresholds does not decrease income inequality, indicating that the income inequality–reducing impact holds at lower levels of debt–to–GDP ratio. This evidence is insensitive to different indicators of income inequality and debts. Findings from this study show how increasing indebtedness contributes to widening income inequality in Africa.