Nonparametric Estimation Research Articles

Nonparametric estimation of mediation effects with a general treatment

. To investigate causal mechanisms, causal mediation analysis decomposes the total treatment effect into the natural direct and indirect effects. This article examines the estimation of the direct and indirect effects in a general treatment effect model, where the treatment can be binary, multi-valued, continuous, or a mixture. We propose generalized weighting estimators with weights estimated by solving an expanding set of equations. Under some sufficient conditions, we show that the proposed estimators are consistent and asymptotically normal. Specifically, when the treatment is discrete, the proposed estimators attain semiparametric efficiency bounds. Meanwhile, when the treatment is continuous, the convergence rates of the proposed estimators are slower than N − 1 / 2 ; however, they are still more efficient than those constructed from the true weighting function. A simulation study reveals that our estimators exhibit satisfactory finite-sample performance, while an application shows their practical value.

Column-Randomized Linear Programs: Performance Guarantees and Applications

Solving Large-Scale Linear Programs by Randomly Sampling Columns Large-scale linear programs (LPs) play a pivotal role in various applications, including the classic cutting-stock problem and the vehicle routing problem. The standard solution approach for these LPs, namely, column generation (CG), is often computationally intractable because of the NP-hard nature of the corresponding subproblem in many applications. In “Column-Randomized Linear Programs: Performance Guarantees and Applications,” Akchen and Mišić introduce a randomized method that involves first sampling a set of columns from the original LP and subsequently solving an LP composed of the sampled columns, termed the column-randomized LP. The authors analyze the optimality gap of the column-randomized LPs and establish conditions under which the gap is small. Empirical findings demonstrate the effectiveness of the column-randomized LP approach, showcasing its advantages over the CG approach in two practical applications: the cutting-stock problem and nonparametric choice model estimation.

Nonparametric estimation and forecasting of interval-valued time series regression models with constraints

Nowadays information technology advances allow the collecting and storage of large complex datasets in many areas. Modeling and forecasting interval-valued time series (ITS) has drawn much attention over the last two decades because interval-valued observations contain more information than point-valued observations over the same period and remove undesirable noises in high-frequency data. However, most work mainly focuses on modeling a linear univariate ITS or bivariate point process. This paper proposes nonparametric regression models for interval-valued time series with imposing constraints, e.g., monotonicity. This setting with a monotonic constraint is consistent with the existing literature, which focuses on incorporating valuable empirical information in modeling and forecasts. Two constraint estimators are developed and asymptotic properties are established. Monte Carlo simulation is conducted to show the finite sample performance. An empirical application to equity premium documents that the proposed model yields a better forecast performance than some popular models in the literature.

Determinants of Ecological Footprint: A Quantile Regression Approach

Through the examination of the ecological consequences of human actions, policymakers are able to distinguish certain areas in which resource use can be increased and the generation of waste diminished. This study examines the effects of foreign direct investment, gross domestic product, industrialization, renewable energy consumption, and urban population on the ecological footprints in 131 countries between 1997 and 2020. The objective of this study is to establish a thorough understanding of the relationship between these variables and ecological footprints while considering temporal changes from economic and environmental aspects. The analysis of a substantial dataset encompassing many countries aims to uncover recurring patterns and trends that can provide valuable information for the formulation of policies and strategies pertaining to sustainable development on a global level. The study fills a significant gap in the knowledge on the ecological impact of different variables, providing a nuanced understanding of the interdependencies among these factors, thus guiding sustainable development strategies, and promoting global sustainability. The study utilizes quantile regression analysis, a nonparametric estimator, to estimate consistent coefficients. The statistical analysis reveals that FDI, urbanization, and GDP have statistically significant and positive effects on ecological footprints. Industrialization and renewable energy consumption show significant and negative relationships with ecological footprints. The findings of this study contribute to the understanding of the relationships among these variables and provide insight to inform policy and decision-making efforts focused on reducing ecological consequences and advancing sustainable development goals.

Estimation of Weighted Extropy with Focus on Its Use in Reliability Modeling.

In the literature, estimation of weighted extropy is infrequently considered. In this paper, some non-parametric estimators of weighted extropy are given. The validation and comparison of the estimators are implemented with the help of simulation study and data illustration. The usefulness of the estimators is demonstrated using real data sets.

A Comprehensive Analysis of MSE in Estimating Conditional Hazard Functions: A Local Linear, Single Index Approach for MAR Scenarios

In unveiling the non-parametric estimation of the conditional hazard function through the local linear method, our study yields key insights into the method’s behavior. We present rigorous analyses demonstrating the mean square convergence of the estimator, subject to specific conditions, within the realm of independent observations with missing data. Furthermore, our contributions extend to the derivation of expressions detailing both bias and variance of the estimator. Emphasizing the practical implications, we underscore the applicability of two distinct models discussed in this paper for single index estimation scenarios. These findings not only enhance our understanding of survival analysis methodologies but also provide practitioners with valuable tools for navigating the complexities of missing data in the estimation of conditional hazard functions. Ultimately, our results affirm the robustness of the local linear method in non-parametrically estimating the conditional hazard function, offering a nuanced perspective on its performance in the challenging context of independent observations with missing data.

Nonparametric estimation of extropy based measures under right censoring

Nonparametric estimation of extropy based measures under right censoring

A new non-parametric estimation of the expected shortfall for dependent financial losses

In this paper, we address the problem of kernel estimation of the Expected Shortfall (ES) risk measure for financial losses that satisfy the α-mixing conditions. First, we introduce a new non-parametric estimator for the ES measure using a kernel estimation. Given that the ES measure is the sum of the Value-at-Risk and the mean-excess function, we provide an estimation of the ES as a sum of the estimators of these two components. Our new estimator has a closed-form expression that depends on the choice of the kernel smoothing function, and we derive these expressions in the case of Gaussian, Uniform, and Epanechnikov kernel functions. We study the asymptotic properties of this new estimator and compare it to the Scaillet estimator. Capitalizing on the properties of these two estimators, we combine them to create a new estimator for the ES which reduces the bias and lowers the mean square error. The combined estimator shows better stability with respect to the choice of the kernel smoothing parameter. Our findings are illustrated through some numerical examples that help us to assess the small sample properties of the different estimators considered in this paper.

Multivariate Density Estimation by Neural Networks.

We propose nonparametric methods to obtain the Probability Density Function (PDF) to assess the properties of the underlying data generating process (DGP) without imposing any assumptions on the DGP, using neural networks (NNs). The proposed NN has advantages compared to well-known parametric and nonparametric density estimators. Our approach builds on literature on cumulative distribution function (CDF) estimation using NN. We extend this literature by providing analytical derivatives of this obtained CDF. Our approach hence removes the numerical approximation error in differentiating the CDF output, leading to more accurate PDF estimates. The proposed solution applies to any NN model, i.e., for any number of hidden layers or hidden neurons in the multilayer perceptron (MLP) structure. The proposed solution applies the PDF estimation by NN to continuous distributions as well as discrete distributions. We also show that the proposed solution to obtain the PDF leads to good approximations when applied to correlated variables in a multivariate setting. We test the performance of our method in a large Monte Carlo simulation using various complex distributions. Subsequently, we apply our method to estimate the density of the number of vehicle counts per minute measured with road sensors for a time window of 24 h.

The role of cytoreductive nephrectomy (CN) in the immune checkpoint inhibitor (ICI) era of metastatic renal cell carcinoma (mRCC): A systematic review and individual patient data (IPD) meta-analysis of 2319 patients.

425 Background: The combination of CN and systemic therapy has been established as one of the mainstay treatments for mRCC during the targeted therapy era. However, the role of CN in the ICI era remains unclear. Methods: We performed a systematic search of the MEDLINE, EMBASE, and Web of Science databases until August 26th, 2023, for studies comparing the combination of CN + ICI vs. ICI alone in mRCC. Using published Kaplan-Meier overall survival (OS) curves, we reconstructed IPD and then performed one-stage and two-stage meta-analyses with both parametric and non-parametric effect estimates. To account for immortal time bias, we performed 6-month and 12-month landmark analyses. We also performed a subgroup analysis according to ICI line of treatment. The risk of bias was assessed using the ROBINS-I tool. Results: We identified eight retrospective cohort studies fulfilling our inclusion criteria. Only two out of eight studies adjusted for immortal time bias and none of them adequately adjusted for all predetermined confounding factors. A total of 2319 (1264 CN + ICI and 1055 ICI only) patients were included in our analysis. Patients in CN + ICI group were younger (median age 58.2 vs. 62.8), had lower proportions of non-clear cell histology (8.8% vs. 15.2%), ≥2 metastatic sites (60.0% vs. 68.5%), liver metastases (9.0% vs. 21.9%), and poor IMDC risk score (21.7% vs. 43.9%), but had higher proportions of sarcomatoid histology (15.6% vs. 10.6%) and ≥2nd line treatment (38.1% vs. 17.1%). The combination of CN + ICI was associated with superior OS in the one stage (HR: 0.45, 95% CI 0.38–0.52), 6-month landmark (HR: 0.45, 95% CI 0.37–0.54), 12-month landmark (HR: 0.50, 95% CI 0.31–0.50) and two-stage (HR: 0.38, 95% CI 0.29–0.49) meta-analyses. Similarly, the combination of CN + ICI was associated with superior OS in the subgroup of patients receiving first-line ICI (HR 0.39, 95% CI: 0.30–0.48). Conclusions: The combination of CN + ICI for mRCC may be associated with superior OS compared to ICI alone, but currently available data are subject to selection bias. More studies, including well-designed randomized controlled trials, are needed to determine the role of CN in the ICI era. [Table: see text]

Nonparametric Estimation for Multi-server Queues Based on the Number of Clients in the System

Nonparametric Estimation for Multi-server Queues Based on the Number of Clients in the System

Nonparametric assessment of two-dimensional density of nonlinear location signal distribution for object recognition despite background noise

Problem statement Searching for objects in shelter environments is a challenge associated with the difficulty of obtaining and interpreting search results. Currently, within the statistical theory of detection and recognition, no models and methods have been developed that allow automatically identifying the detected object. This is due to the difficulty of describing signal and noise models in the form of known statistical distributions. The variety of signals leads to the inability to describe them by any universal law of distribution. Therefore, traditional detection and recognition criteria do not provide high reliability of object search and identification. The purpose of the study. To develop and test the method for nonparametric estimation of nonlinear location signals, assess the potential possibilities of applying the developed method for automatic (automated) signal detection (recognition) systems. Results. The model for recognizing nonlinear location signals based on nonparametric approximation of two-dimensional probability distribution densities is presented. The potential possibility of improving the efficiency of nonlinear locators is shown. Practical significance. For nonlinear location systems a toolkit for estimating the probability of the detected object belonging to a given class of objects is proposed.

Analysis of optimization methods for nonparametric estimation of probability density in large samples

Analysis of optimization methods for nonparametric estimation of probability density in large samples

Optimization of functional diagnostic test: the effect of kernel method as an estimator of ROC curve

Technical development over the last few decades has resulted in the emergence of complex data, in many cases functional data (FD). This type of data can emerge in many medical studies which are geared towards detecting diseases, predicting their course or evaluating the response to a therapy, to name a few. Thus, it is very useful to have statistical methods enabling us to evaluate diagnostic tests based on functional biomarkers. In fact, a diagnostic test that uses functional variables as biomarkers has been developed recently. Their authors proposed a functional version of ROC analysis, resulting in an empirical estimate of the functional ROC curve. In order to improve this methodology, the present paper proposes a procedure to obtain a smooth version of non-parametric estimator of the ROC curve. In addition, a comprehensive simulation study lets to investigate the discriminatory and predictive abilities of the resulting functional diagnostic test. Two examples with real medical data illustrate the approach developed: one deals with gene expression levels for tumoural/normal samples of prostate cancer; the other dataset is about white matter structures in the brain in multiple sclerosis patients.

Improved Hybrid Approach for Enhancing Protein Coding Regions Identification in DNA Sequences

Introduction: Identifying and predicting protein-coding regions within DNA sequences play a pivotal role in genomic research. This paper introduces an approach for identifying proteincoding regions in DNA sequences, employing a hybrid methodology that combines a digital bandpass filter with wavelet transforms and various spectral estimation techniques to enhance exon prediction. Specifically, the Haar and Daubechies wavelet transforms are applied to improve the accuracy of protein-coding region (exon) prediction, enabling the extraction of intricate details that may be obscured in the original DNA sequences. background: The identification and prediction of protein-coding regions within DNA sequences play a pivotal role in genomic research. Methods: This research showcases the utility of Haar and Daubechies wavelet transforms, both nonparametric and parametric spectral estimation methods, and the deployment of a digital band pass filter for detecting peaks in exon regions. Additionally, the application of the Electron-Ion Interaction Potential (EIIP) method for converting symbolic DNA sequences into numerical values and the utilization of sum-of-sinusoids (SoS) mathematical models with optimized parameters further enrich the toolbox for DNA sequence analysis, ensuring the success of this proposed method in modeling DNA sequences optimally and accurately identifying genes. objective: Enhanced Protein-Coding Region Identification in DNA Sequences Using Wavelet Transforms Results: The outcomes of this approach showcase a substantial enhancement in identification accuracy for protein-coding regions. In terms of peak location detection, the application of Haar and Daubechies wavelet transforms enhances the accuracy of peak localization by approximately (0.01, 3-5 dB). When employing non-parametric and parametric spectral estimation techniques, there is an improvement in peak location by approximately (0.01, 4 dB) compared to the original signal. The proposed approach also achieves higher accuracy when compared with existing methods. method: hybrid methodology that combines a digital band-pass filter with wavelet transforms and various spectral estimation techniques to enhance exon prediction. Conclusion: These findings not only bridge gaps in DNA sequence analysis but also offer a promising pathway for advancing exonic region prediction and gene identification in genomics research. The hybrid methodology presented stands as a robust contribution to the evolving landscape of genomic analysis techniques. result: The results obtained through this proposed method demonstrate significantly improved identification accuracy. These findings offer a promising avenue for DNA sequence analysis, exonic region prediction, and gene identification.

Economic performance and carbon emissions: revisiting the role of tourism and energy efficiency for BRICS economies

AbstractIncreased demands for infrastructure, water, electricity, and different natural assets have triggered land erosion, climate change, and pollution increase and deterioration in biodiversity. The purpose of this research is to look at how economic performance, tourism, renewable energy, and energy efficiency affect carbon emissions in the emerging economies of BRICS during 1990–2021. Using panel estimation approaches, the empirical outcomes validate the longer-run equilibrium connection between the components of the model. Using a nonparametric estimator, the study found that economic performance is the significant driver of higher emissions levels in the sample countries. In contrast, tourism, energy efficiency, and renewable energy substantially reduce emissions levels and improve environmental sustainability. The estimated results have been found robust, and the feedback effect is found valid between repressors and carbon emissions. This study further suggests that investment in research and development, improvement in energy-efficient tools and equipment utilization, and enhanced renewable energy output are the key policy efforts for ensuring environmental sustainability.

Proportional rates models for multivariate panel count data.

Multivariate panel count data arise when there are multiple types of recurrent events, and the observation for each study subject consists of the number of recurrent events of each type between two successive examinations. We formulate the effects of potentially time-dependent covariates on multiple types of recurrent events through proportional rates models, while leaving the dependence structures of the related recurrent events completely unspecified. We employ nonparametric maximum pseudo-likelihood estimation under the working assumptions that all types of events are independent and each type of event is a nonhomogeneous Poisson process, and we develop a simple and stable EM-type algorithm. We show that the resulting estimators of the regression parameters are consistent and asymptotically normal, with a covariance matrix that can be estimated consistently by a sandwich estimator. In addition, we develop a class of graphical and numerical methods for checking the adequacy of the fitted model. Finally, we evaluate the performance of the proposed methods through simulation studies and analysis of a skin cancer clinical trial.

Incorporating the neutrosophic framework into kernel regression for predictive mean estimation

In traditional statistics, all research endeavors revolve around utilizing precise, crisp data for the predictive estimation of population mean in survey sampling, when the supplementary information is accessible. However, these types of estimates often suffer from bias. The major aim is to uncover the most accurate estimates for the unknown value of the population mean while minimizing the mean square error (MSE). We have employed the neutrosophic approach, which is the extension of classical statistics that deals with the uncertain, vague, and indeterminate information, and proposed a neutrosophic predictive estimator of finite population mean using the kernel regression. The proposed estimator does not yield a single numerical value but instead provides an interval range within which the population parameter is likely to exist. This approach enhances the efficiency of the estimators by offering an estimated interval that encompasses the unknown value of the population mean with the least possible mean squared error (MSE). The simulation-based efficiency of the proposed estimator is discussed using the Sine, Bump and real-time temperature data set of Islamabad by using symmetric (Gaussian) kernel. The proposed non-parametric neutrosophic estimator has shown more effective results under the various bandwidth selectors than the adapted neutrosophic estimators.

Non-plug-in estimators could outperform plug-in estimators: a cautionary note and a diagnosis

Abstract Objectives Highly flexible nonparametric estimators have gained popularity in causal inference and epidemiology. Popular examples of such estimators include targeted maximum likelihood estimators (TMLE) and double machine learning (DML). TMLE is often argued or suggested to be better than DML estimators and several other estimators in small to moderate samples – even if they share the same large-sample properties – because TMLE is a plug-in estimator and respects the known bounds on the parameter, while other estimators might fall outside the known bounds and yield absurd estimates. However, this argument is not a rigorously proven result and may fail in certain cases. Methods In a carefully chosen simulation setting, I compare the performance of several versions of TMLE and DML estimators of the average treatment effect among treated in small to moderate samples. Results In this simulation setting, DML estimators outperforms some versions of TMLE in small samples. TMLE fluctuations are unstable, and hence empirically checking the magnitude of the TMLE fluctuation might alert cases where TMLE might perform poorly. Conclusions As a plug-in estimator, TMLE is not guaranteed to outperform non-plug-in counterparts such as DML estimators in small samples. Checking the fluctuation magnitude might be a useful diagnosis for TMLE. More rigorous theoretical justification is needed to understand and compare the finite-sample performance of these highly flexible estimators in general.

From local to global gene co-expression estimation using single-cell RNA-seq data.

In genomics studies, the investigation of gene relationships often brings important biological insights. Currently, the large heterogeneous datasets impose new challenges for statisticians because gene relationships are often local. They change from one sample point to another, may only exist in a subset of the sample, and can be nonlinear or even nonmonotone. Most previous dependence measures do not specifically target local dependence relationships, and the ones that do are computationally costly. In this paper, we explore a state-of-the-art network estimation technique that characterizes gene relationships at the single cell level, under the name of cell-specific gene networks. We first show that averaging the cell-specific gene relationship over a population gives a novel univariate dependence measure, the averaged Local Density Gap (aLDG), that accumulates local dependence and can detect any nonlinear, nonmonotone relationship. Together with a consistent nonparametric estimator, we establish its robustness on both the population and empirical levels. Then, we show that averaging the cell-specific gene relationship over mini-batches determined by some external structure information (eg, spatial or temporal factor) better highlights meaningful local structure change points. We explore the application of aLDG and its minibatch variant in many scenarios, including pairwise gene relationship estimation, bifurcating point detection in cell trajectory, and spatial transcriptomics structure visualization. Both simulations and real data analysis show that aLDG outperforms existing ones.