Nonparametric Statistical Inference Research Articles

Nonparametric statistical inference for compound models

This paper deals with the statistical inference in compound models, which are defined as a sum of i.i.d. random variables ξ 1 + ⋯ + ξ N , where the number of summands, N, is a random variable independent of ξ 1 , ξ 2 , … Using the novel technique based on the superposition of the Mellin and Laplace transforms, we construct a nonparametric estimator for the distribution of N, assuming that the distribution of ξ is known explicitly. Unlike most papers on this topic, we consider the general setting, where the distribution of N is not necessarily of Poisson type.

Nonparametric statistical inference for stochastic optimal control problems and its applications for financial investment

Against a backdrop of financial decision-making, this study examines nonparametric statistical inference problems in stochastic optimal control problems. First, we construct a nonparametric estimation model using the wavelet estimation method for drift and diffusion coefficients. In this study, we focus on stochastic linear–quadratic (SLQ) problems, solved using Riccati equations, and apply this to a cash management problem within the linear–quadratic framework. The results show the effectiveness of the wavelet method using a numerical case.

An innovative machine learning workflow to research China’s systemic financial crisis with SHAP value and Shapley regression

This study proposed a cutting-edge, multistep workflow and upgraded it by addressing its flaw of not considering how to determine the index system objectively. It then used the updated workflow to identify the probability of China’s systemic financial crisis and analyzed the impact of macroeconomic indicators on the crisis. The final workflow comprises four steps: selecting rational indicators, modeling using supervised learning, decomposing the model’s internal function, and conducting the non-linear, non-parametric statistical inference, with advantages of objective index selection, accurate prediction, and high model transparency. In addition, since China’s international influence is progressively increasing, and the report of the 19th National Congress of the Communist Party of China has demonstrated that China is facing severe risk control challenges and stressed that the government should ensure that no systemic risks would emerge, this study selected China’s systemic financial crisis as an example. Specifically, one global trade factor and 11 country-level macroeconomic indicators were selected to conduct the machine learning models. The prediction models captured six risk-rising periods in China’s financial system from 1990 to 2020, which is consistent with reality. The interpretation techniques show the non-linearities of risk drivers, expressed as threshold and interval effects. Furthermore, Shapley regression validates the alignment of the indicators. The final workflow is suitable for categorical and regression analyses in several areas. These methods can also be used independently or in combination, depending on the research requirements. Researchers can switch to other suitable shallow machine learning models or deep neural networks for modeling. The results regarding crises could provide specific references for bank regulators and policymakers to develop critical measures to maintain macroeconomic and financial stability.

Geometric imperfections in CFS structural members, Part II: Data-driven modeling and probabilistic validation

This paper is the second part in a two-part series that examines the role of geometric imperfections in load–displacement response and collapse behavior of cold-formed steel (CFS) structural members. In part I (Farzanian et al., 2023) a review of the basics and a summary of efforts geared towards modeling geometric imperfections was provided. This included the ingredients needed for systematic identification of elastic buckling mode shapes, due to their frequent use in approximating geometric imperfections, and the development of high fidelity shell finite element (FE) nonlinear collapse analysis of CFS members seeded with different geometric imperfection models. Part II is the companion to the analysis in part I that revealed a noticeable variability in the collapse behavior and load carrying capacity of CFS members as a result of adopting different imperfection modeling strategies. In this part we provide the necessary steps to build a probabilistic framework that rests on machine learning, polynomial approximation, and parametric and non-parametric statistical inference and uses imperfection data to build a consistent stochastic field model of geometric imperfections. This data-driven model is then used to generate the much needed realizations of geometric imperfections that are faithful to the underlying statistics of measured data and therefore can be seeded, directly, in nonlinear collapse analysis of CFS members. Nonlinear shell FE analysis, within a stochastic simulation framework, is finally used to (statistically) quantify the impact of geometric imperfections and to enable probabilistic validation of geometric imperfection models.

A Case for Nonparametrics

ABSTRACT We provide a case study for motivating and teaching nonparametric statistical inference alongside traditional parametric approaches. The case consists of analyses by Bracht et al. who use analysis of variance (ANOVA) to assess the applicability of the human microfibrillar-associated protein 4 (MFAP4) as a biomarker for hepatic fibrosis in hepatitis C patients. We revisit their analyses and consider two nonparametric approaches: Mood’s median test and the Kruskal-Wallis test. We demonstrate how this case study enables instructors to discuss critical assumptions of parametric procedures while comparing and contrasting the results of multiple approaches. Interestingly, only one of the three approaches creates groupings that match the treatment recommendations of the European Association for the Study of the Liver (EASL). We provide guidance and resources to aid instructors in directing their students through this case study at various levels, including R code and novel R shiny applications for conducting the analyses in the classroom. Supplementary materials for this article are available online.

Variable Selection with Scalable Bootstrapping in Generalized Linear Model for Massive Data

Bootstrapping is commonly used as a tool for non-parametric statistical inference to assess the quality of estimators in variable selection models. However, for a massive dataset, the computational requirement when using bootstrapping in variable selection models (BootVS) can be crucial. In this study, we propose a novel framework using a bag of little bootstraps variable selection (BLBVS) method with a ridge hybrid procedure to assess the quality of estimators in generalized linear models with a regularized term, such as lasso and group lasso penalties. The proposed method can be easily and naturally implemented with distributed computing, and thus has significant computational advantages for massive datasets. The simulation results show that our novel BLBVS method performs excellently in both accuracy and efficiency when compared with BootVS. Real data analyses including regression on a bike sharing dataset and classification of a lending club dataset are presented to illustrate the computational superiority of BLBVS in large-scale datasets.

Multivariate ranks based on randomized lift-interdirections

Every multivariate sign and rank test needs a workable concept of ranks for multivariate data. Unfortunately, multidimensional spaces lack natural ordering and, consequently, there are no universally accepted ways how to rank vector observations. Existing proposals usable beyond small dimensions are very few in number, and each of them has its own advantages and drawbacks. Therefore, new multivariate ranks based on randomized lift-interdirections are presented, discussed and investigated. These naturally robust and invariant hyperplane-based ranks can be computed quickly and easily even in relatively high-dimensional spaces, and they can be used for nonparametric statistical inference in some existing optimal statistical procedures without altering their asymptotic behavior under null hypotheses or changing their performance under local alternatives. This is not only proved theoretically in case of the canonical sign and rank one-sample test for elliptically distributed observations, but also illustrated empirically in a small simulation study.

Multivariate elliptical-based Birnbaum–Saunders kernel density estimation for nonnegative data

The Birnbaum–Saunders distribution has been generalized in various ways, for parametric or nonparametric statistical inference. In this paper, as a remedy for the boundary bias problem of nonparametric density estimation, a family of deformed multivariate elliptical-based non-central Birnbaum–Saunders kernel density estimators is introduced, and its asymptotic mean integrated squared error is discussed. The simulation results reveal that a novel log-elliptical density estimator has a good performance in small sample size.

Gut Microbiota Dynamics in Natural Populations of Pintomyia evansi under Experimental Infection with Leishmania infantum.

Pintomyia evansi is recognized by its vectorial competence in the transmission of parasites that cause fatal visceral leishmaniasis in rural and urban environments of the Caribbean coast of Colombia. The effect on and the variation of the gut microbiota in female P. evansi infected with Leishmania infantum were evaluated under experimental conditions using 16S rRNA Illumina MiSeq sequencing. In the coinfection assay with L. infantum, 96.8% of the midgut microbial population was composed mainly of Proteobacteria (71.0%), followed by Cyanobacteria (20.4%), Actinobacteria (2.7%), and Firmicutes (2.7%). In insect controls (uninfected with L. infantum) that were treated or not with antibiotics, Ralstonia was reported to have high relative abundance (55.1–64.8%), in contrast to guts with a high load of infection from L. infantum (23.4–35.9%). ASVs that moderately increased in guts infected with Leishmania were Bacillus and Aeromonas. Kruskal–Wallis nonparametric variance statistical inference showed statistically significant intergroup differences in the guts of P. evansi infected and uninfected with L. infantum (p < 0.05), suggesting that some individuals of the microbiota could induce or restrict Leishmania infection. This assay also showed a negative effect of the antibiotic treatment and L. infantum infection on the gut microbiota diversity. Endosymbionts, such as Microsporidia infections (<2%), were more often associated with guts without Leishmania infection, whereas Arsenophonus was only found in guts with a high load of Leishmania infection and treated with antibiotics. Finally, this is the first report that showed the potential role of intestinal microbiota in natural populations of P. evansi in susceptibility to L. infantum infection.

Driving effect of CO2 emissions on economic growth—application of empirical likelihood for generalized method of moments

In this paper, the panel data of 19 out of 21 APEC members from 1993 to 2018 is selected as a research sample. Firstly, based on the extended Cobb-Douglas production function, the relationship between CO2 emissions and economic growth is explored via the panel data methods, which fully consider the endogeneity between variables and the unobserved individual heterogeneity. Secondly, to examine the driving effect of CO2 emissions on economic growth, the Empirical Likelihood for Generalized method of moments with nonparametric estimation characteristics is utilized to calculate the returns on economic scale and the corresponding confidence interval. The results show that CO2 emissions have a significant positive impact on economic growth. Moreover, the confidence interval of returns to economic scale is very small, indicating current levels of CO2 emissions have reached the limit to drive economic growth when the technical level, labor employment, capital, urbanization, trade, and other factors tend to stabilize. Finally, some recommendations were presented to achieve sustainable development goals. Highlights In combination with the extended Cobb-Douglas production function theory, employs 2SLS and GMM method that takes unobserved the heterogeneity between regions and endogeneity between variables in consideration to explore the relationship between CO2 emissions for economic growth. The extended model of the GMM-Empirical Likelihood for Generalized Moment Method (GMEL) is used to investigate whether the Driving effect of CO2 emissions on Economic Growth reaching its limit or not? Selected the panel data of APEC countries or regions as the research samples, which has never been studied by scholars. The GMEL is a non-parametric statistical inference method that has higher estimation accuracy than the traditional parametric estimation method. The confidence interval constructed by the GMEL method has the advantages of domain retention, transformation invariance.

Characterization of histone modification patterns and prediction of novel promoters using functional principal component analysis.

Characterization of distinct histone methylation and acetylation binding patterns in promoters and prediction of novel regulatory regions remains an important area of genomic research, as it is hypothesized that distinct chromatin signatures may specify unique genomic functions. However, methods that have been proposed in the literature are either descriptive in nature or are fully parametric and hence more restrictive in pattern discovery. In this article, we propose a two-step non-parametric statistical inference procedure to characterize unique histone modification patterns and apply it to analyzing the binding patterns of four histone marks, H3K4me2, H3K4me3, H3K9ac, and H4K20me1, in human B-lymphoblastoid cells. In the first step, we used a functional principal component analysis method to represent the concatenated binding patterns of these four histone marks around the transcription start sites as smooth curves. In the second step, we clustered these curves to reveal several unique classes of binding patterns. These uncovered patterns were used in turn to scan the whole-genome to predict novel and alternative promoters. Our analyses show that there are three distinct promoter binding patterns of active genes. Further, 19654 regions not within known gene promoters were found to overlap with human ESTs, CpG islands, or common SNPs, indicative of their potential role in gene regulation, including being potential novel promoter regions.

PM2.5 Concentration Measurement Analysis by Using Non-Parametric Statistical Inference

Rapid population growth, urbanization and motorization have brought about secondary effects that have gradually damaged the atmosphere, whose importance is vital for both the survival of all living beings and the climate balance. In this sense, air pollution is a problem that affects current society and is much more critical in developing countries. In this context, in the present paper non-parametric statistical inference techniques are used to carry out the analysis of measurements of health concerning fine particulate matter concentration, PM2.5, in an urban park of Quito, Ecuador. In short, the data collected during the measurements were stored in random variables and the Kruskal-Wallis test was used to test if these random variables come from populations with identical distributions. Also, the Wilcoxon signed rank test was used to test if the numerical values collected in the samples of the random variables of interest represent a level of contamination that could be dangerous for human beings. The experimental results show that urban parks and, specifically, trees are a natural filter between the pollution generated in the road and the center of the park. Therefore, the role of trees in the face of vehicular pollution will depend on two variables: the amount and compactness of the vegetation, and the emission levels recorded in the border roads.

Analysis of the Information Obtained From PM2.5 Concentration Measurements in an Urban Park

In this article, parametric and nonparametric statistical inference analysis of a set the measurements of air pollution because of PM2.5 concentrations was performed. The research work was carried out in an urban park in Quito, Ecuador. Specifically, the park that was chosen to perform the analysis was La Carolina Park. The analysis carried out here was aimed at obtaining the statistical models for parts of this urban park under study and some of its border streets. Furthermore, the park and its border streets were modeled as random variables that were finally classified according to the amount of PM2.5 concentration levels they carry. This classification was performed by using a method based on both Friedman’s test and the categories of the index of air quality of Quito. The results of this article showed that air pollution levels because of PM2.5 concentrations in La Carolina Park are not in alert level. The worst case, considering the analysis tools used in this article, is that one of the streets that border the park is in caution level. The other streets and parts of the park that were analyzed are either in a desirable level or in an acceptable level. Furthermore, in this article, it has been shown that as pedestrian and temporary residents move further away from the trees and vegetation of the park, the level of exposure to PM2.5 concentrations that they experience is higher.

A Comparative Study of the Power of Parametric and Permutation Tests for a Multidimensional Two-sample Location Problem

Objective: A comparison of multidimensional populations is a very interesting and common statistical problem. It most often involves verifying a hypothesis about the equality of mean vectors in two populations. The classical test for verification of this hypothesis is the Hotelling’s T 2 test. Another solution is to use simulation and randomization methods to test the significance of differences between the studied populations. Permutation tests are to enable statistical inference in situations where it is not possible to use classical parametric tests. These tests are supposed to provide comparable power to parametric tests with a simultaneous reduction of assumptions, e.g. regarding the sample size taken or the distribution of the tested variable in the population. The purpose of this study is a comparative analysis of the parametric test, the (usual) permutation test, and the nonparametric permutation procedure using two-stage ASL determination. Research Design & Methods: The study considered the analysis of multivariate data. The paper presents theoretical considerations and refers to the Monte Carlo simulation. Findings: The article presents a permutational, complex procedure for assessing the overall ASL (achieved significance level) value. The applied nonparametric statistical inference procedure uses combining functions. A simulation study was carried out to determine the size and power of the test under normality. A Monte Carlo simulation made it possible to compare the empirical power of this test with that of Hotelling’s T 2 test. The most powerful test was the permutation test based on a two-stage ASL determination method using the Fisher combining function. Implications/Recommendations: The advantage of the proposed method is that it can be used even when samples are taken from any type of continuous distributions in a population. Contribution: The proposed test can be used in the analysis of multidimensional economic phenomena.

Spectral stochastic isogeometric analysis for linear stability analysis of plate

A spectral stochastic isogeometric analysis (SSIGA) scheme is proposed for the stochastic linear stability analysis of plate with uncertain material properties. Within the proposed SSIGA scheme, the first-order shear deformation theory of plate is adopted for modelling the kinematic relationship. Both homogeneous and functionally graded material (FGM) models can be incorporated. The considered spatially dependent uncertainties (i.e., Young’s modulus and Poisson’s ratio) are modelled as random fields with Gaussian and lognormal distributions, and the spatially independent uncertainty (i.e., gradient index of FGM) is modelled as random variable. The generalized isogeometric basis function is adopted for both the random field geometry representation and random field discretization through the Karhunen–Loève (K–L) expansion. An extended support vector regression (X-SVR) with a new generalized Gegenbauer polynomial kernel is developed to model the nonlinear relationship between the structural uncertainties and the buckling load. By further implementing various nonparametric statistical inference methods, the mean, standard deviation, probability density function (PDF), and cumulative distribution function (CDF) of the buckling load can be effectively established to determine the strength limit of the plate. The accuracy, efficiency, and applicability of the proposed approach are illustrated through two numerical examples.

Nonparametric statistical inference for drift vector fields of multi-dimensional diffusions

The problem of determining a periodic Lipschitz vector field $b=(b_1, \dots, b_d)$ from an observed trajectory of the solution $(X_t: 0 \le t \le T)$ of the multi-dimensional stochastic differential equation \begin{equation*} dX_t = b(X_t)dt + dW_t, \quad t \geq 0, \end{equation*} where $W_t$ is a standard $d$-dimensional Brownian motion, is considered. Convergence rates of a penalised least squares estimator, which equals the maximum a posteriori (MAP) estimate corresponding to a high-dimensional Gaussian product prior, are derived. These results are deduced from corresponding contraction rates for the associated posterior distributions. The rates obtained are optimal up to log-factors in $L^2$-loss in any dimension, and also for supremum norm loss when $d \le 4$. Further, when $d \le 3$, nonparametric Bernstein-von Mises theorems are proved for the posterior distributions of $b$. From this we deduce functional central limit theorems for the implied estimators of the invariant measure $\mu_b$. The limiting Gaussian process distributions have a covariance structure that is asymptotically optimal from an information-theoretic point of view.

Individual-level performance of nature reserves in forest protection and the effects of management level and establishment age

Many studies have evaluated the overall effectiveness of protected areas (PAs) in halting deforestation from a perspective of the entire PA system. However, few studies assess PA performance at an individual level, and investigate the effects of management level and establishment age of PAs. With nature reserves (NRs) in southwest China as the case, we set an independent control area (CA) for each NR 10-km away from its boundary to avoid the spillover effect. Forested pixels at least 300 m apart were then sampled within each NR and its CA. We applied the Propensity Score Matching method with five control variables to balance the heterogeneity of land characteristics between NR and CA sample pixels. Based on the matched samples for each NR, the individual effectiveness of 137 NRs between 2001 and 2012 was quantified. We then compared the effects of NRs with different management levels (national and provincial) and establishment ages (designated between 1981–1990 and 1991–2000) by means of nonparametric test and statistical inference. We found that approximately 63% of the NRs suffered less deforestation within their boundaries than in adjacent CAs. National NRs were more effective than provincial NRs in curbing deforestation, but age had little bearing on the effectiveness of NRs. Our results revealed that NRs could play a prominent role in the greening trends of southwest China. This study offers the first individual-level assessment on NR effectiveness for forest protection in southwest China, which helps provide a more solid support for promoting effective NR management.

Nonparametric Versus Parametric Reasoning Based on Contingency Tables

This paper proposes scenarios of generating two-way and three way contingency tables (CTs). A concept of probability flow parameter (PFP) plays a crucial role in these scenarios. Additionally, measures of untruthfulness of H0 are defined. The power divergence statistics and the |X| statistics are used. This paper is a simple attempt to replace a nonparametric statistical inference from CTs by the parametric one. Maximum likelihood method is applied to estimate PFP and instructions of generating CTs according to scenarios in question are presented. The Monte Carlo method is used to carry out computer simulations.

Statistical nonparametric mapping: Multivariate permutation tests for location, correlation, and regression problems in neuroimaging

Nonparametric statistical inference via permutation testing is on the rise in neuroimaging research. This rise in popularity is likely in response to recent studies that have demonstrated limitations of parametric inference in certain situations. Nonparametric tests have the appeal of requiring fewer assumptions than their parametric counterparts, and are often touted as being more flexible and more useful for small samples. Furthermore, recent studies have demonstrated the robustness of nonparametric methods in situations when parametric inference fails. As a result, many nonstatistical neuroimaging researchers are likely to believe that nonparametric permutation tests are always a “safe choice” because the results do not depend on distributional assumptions and/or large sample approximations. Alas, this commonly held belief is not entirely accurate, given that nonparametric tests still do rely on assumptions and/or approximations for valid statistical inference. When these assumptions are met, nonparametric permutation tests have the potential to produce valid inferential results for the intended hypotheses. However, as I demonstrate, when these assumptions are violated, nonparametric permutation tests can produce invalid and/or misleading results, which have important implications for the use of such methods in neuroimaging research. All hope is not lost though, as recent theoretical developments in nonparametric statistics can improve current implementations of permutation tests in neuroimaging research.This article is categorized under: Statistical and Graphical Methods of Data Analysis &gt; Nonparametric Methods Statistical and Graphical Methods of Data Analysis &gt; Bootstrap and Resampling Data: Types and Structure &gt; Image and Spatial Data

Bernstein–von Mises theorems for statistical inverse problems II: compound Poisson processes

We study nonparametric Bayesian statistical inference for the parameters governing a pure jump process of the form $$Y_t = \sum_{k=1}^{N(t)} Z_k,~~~ t \ge 0,$$ where $N(t)$ is a standard Poisson process of intensity $\lambda$, and $Z_k$ are drawn i.i.d.~from jump measure $\mu$. A high-dimensional wavelet series prior for the L\'evy measure $\nu = \lambda \mu$ is devised and the posterior distribution arises from observing discrete samples $Y_\Delta, Y_{2\Delta}, \dots, Y_{n\Delta}$ at fixed observation distance $\Delta$, giving rise to a nonlinear inverse inference problem. We derive contraction rates in uniform norm for the posterior distribution around the true L\'evy density that are optimal up to logarithmic factors over H\"older classes, as sample size $n$ increases. We prove a functional Bernstein-von Mises theorem for the distribution functions of both $\mu$ and $\nu$, as well as for the intensity $\lambda$, establishing the fact that the posterior distribution is approximated by an infinite-dimensional Gaussian measure whose covariance structure is shown to attain the information lower bound for this inverse problem. As a consequence posterior based inferences, such as nonparametric credible sets, are asymptotically valid and optimal from a frequentist point of view.