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In some high-dimensional and semiparametric inference problems involving two populations, the parameter of interest can be characterized by two-sample U-statistics involving some nuisance parameters. In this work we first extend the framework of one-step estimation with cross-fitting to two-sample U-statistics, showing that using an orthogonalized influence function can effectively remove the first order bias, resulting in asymptotically normal estimates of the parameter of interest. As an example, we apply this method and theory to the problem of testing two-sample conditional distributions, also known as strong ignorability. When combined with a conformal-based rank-sum test, we discover that the nuisance parameters can be divided into two categories, where in one category the nuisance estimation accuracy does not affect the testing validity, whereas in the other the nuisance estimation accuracy must satisfy the usual requirement for the test to be valid. We believe these findings provide further insights into and enhance the conformal inference toolbox. [ABSTRACT FROM AUTHOR]

In this paper, we investigate hypothesis testing for the linear combination of mean vectors across multiple populations through the method of random integration. We have established the asymptotic distributions of the test statistics under both null and alternative hypotheses. Additionally, we provide a theoretical explanation for the special use of our test statistics in situations when the nonzero signals in the linear combination of the true mean vectors are weakly dense and nearly the same sign. Moreover, Monte Carlo simulations are presented to evaluate the suggested test against existing high-dimensional tests. The findings from these simulations reveal that our test not only aligns with the performance of other tests in terms of size but also exhibits superior power. [ABSTRACT FROM AUTHOR]

Semivariance is a measure of the dispersion of all observations that fall above the mean or target value of a random variable and it plays an important role in life-length, actuarial and income studies. In this paper, we develop a new non-parametric test for testing the equality of upper semivariance. We use the U-statistic theory to derive the test statistic and then study the asymptotic properties of the test statistic. We also develop a jackknife empirical likelihood (JEL) ratio test for testing the equality of upper semivariance. Extensive Monte Carlo simulation studies are carried out to validate the performance of the proposed JEL-based test. We illustrate the test procedure using real data. [ABSTRACT FROM AUTHOR]

AbstractNeurodegenerative disorders such as Alzheimer’s disease (AD) present a significant global health challenge, characterized by cognitive decline, functional impairment, and other debilitating effects. Current AD clinical trials often assess multiple longitudinal primary endpoints to comprehensively evaluate treatment efficacy. Traditional methods, however, may fail to capture global treatment effects, require larger sample sizes due to multiplicity adjustments, and may not fully utilize the available longitudinal data. To address these limitations, we introduce the Longitudinal Rank Sum Test (LRST), a novel nonparametric rank-based omnibus test statistic. The LRST enables a comprehensive assessment of treatment efficacy across multiple endpoints and time points without the need for multiplicity adjustments, effectively controlling Type I error while enhancing statistical power. It offers flexibility for various data distributions encountered in AD research and maximizes the utilization of longitudinal data. Simulations across realistic clinical trial scenarios, including those with conflicting treatment effects, and real-data applications demonstrate the LRST’s performance, underscoring its potential as a valuable tool in AD clinical trials. [ABSTRACT FROM AUTHOR]

AbstractIn order to improve the estimation efficiency of reliability for a two-component parallel system, this article presents a non parametric estimator of reliability based on ranked set sampling using the idea of U-statistics. The variance of the new estimator is calculated, and it is shown to be smaller than the variance of the corresponding non parametric estimator under simple random sampling. The new estimator is shown to have asymptotic normality, the asymptotic relative efficiency of the new estimator and the corresponding estimator under simple random sampling is analyzed, and the simulated relative efficiencies of small samples are calculated. The research results of estimation efficiencies show that the ranked set sampling method is always more efficient than the simple random sampling method. Finally, an empirical study based on real-life data supports the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

AbstractU-statistics play central roles in many statistical learning tools but face the haunting issue of scalability. Despite extensive research on accelerating computation by U-statistic reduction, existing results almost exclusively focused on power analysis. Little work addresses risk control accuracy, which requires distinct and much more challenging techniques. In this paper, we establish the first statistical inference procedure with provably higher-order accurate risk control for incomplete U-statistics. The sharpness of our new result enables us to reveal how risk control accuracy also trades off with speed, for the first time in literature, which complements the well-known variance-speed trade-off. Our general framework converts the challenging and case-by-case analysis for many different designs into a surprisingly principled and routine computation. We conducted comprehensive numerical studies and observed results that validate our theory’s sharpness. Our method also demonstrates effectiveness on real-world data applications. [ABSTRACT FROM AUTHOR]

In this paper, we study self-normalized moderate deviations for degenerate U-statistics of order 2. Let { X i , i ≥ 1 } be i.i.d. random variables and consider symmetric and degenerate kernel functions in the form h (x , y) = ∑ l = 1 ∞ λ l g l (x) g l (y) , where λ l > 0 , E g l (X 1) = 0 , and g l (X 1) is in the domain of attraction of a normal law for all l ≥ 1 . Under the condition ∑ l = 1 ∞ λ l < ∞ and some truncated conditions for { g l (X 1) : l ≥ 1 } , we show that log P ( ∑ 1 ≤ i ≠ j ≤ n h (X i , X j) max 1 ≤ l < ∞ λ l V n , l 2 ≥ x n 2) ∼ − x n 2 2 for x n → ∞ and x n = o (n) , where V n , l 2 = ∑ i = 1 n g l 2 (X i) . As application, a law of the iterated logarithm is also obtained. [ABSTRACT FROM AUTHOR]

In the present paper, we develop a new goodness of fit test for gamma distribution based on the fixed point characterization. We use U-Statistics theory to derive the test statistic. We discuss how the right censored observations are incorporated into the proposed test. The asymptotic properties of the test statistics in censored and uncensored cases are studied. We carry out a Monte Carlo simulation study to validate the finite sample performance of the proposed tests. We also illustrate the test procedures using real data sets. [ABSTRACT FROM AUTHOR]

The Mann–Whitney–Wilcoxon rank sum test (MWWRST) is a widely used method for comparing two treatment groups in randomized control trials, particularly when dealing with highly skewed data. However, when applied to observational study data, the MWWRST often yields invalid results for causal inference. To address this limitation, Wu et al. (Causal inference for Mann–Whitney–Wilcoxon rank sum and other nonparametric statistics, Stat. Med. 33 (2014), pp. 1261–1271) introduced an approach that incorporates inverse probability weighting (IPW) into this rank-based statistic to mitigate confounding effects. Subsequently, Mao (On causal estimation using U-statistics, Biometrika 105 (2018), pp. 215–220), Zhang et al. (Estimating Mann Whitney-type causal effects, J. Causal Inference 7 (2019), ARTICLE ID 20180010), and Ai et al. (A Mann–Whitney test of distributional effects in a multivalued treatment, J. Stat. Plan. Inference 209 (2020), pp. 85–100) extended this IPW estimator to develop doubly robust estimators. Nevertheless, each of these approaches has notable limitations. Mao's method imposes stringent assumptions that may not align with real-world study data. Zhang et al.'s (Estimating Mann Whitney-type causal effects, J. Causal Inference 7 (2019), ARTICLE ID 20180010) estimators rely on bootstrap inference, which suffers from computational inefficiency and lacks known asymptotic properties. Meanwhile, Ai et al. (A Mann–Whitney test of distributional effects in a multivalued treatment, J. Stat. Plan. Inference 209 (2020), pp. 85–100) primarily focus on testing the null hypothesis of equal distributions between two groups, which is a more stringent assumption that may not be well-suited to the primary practical application of MWWRST. In this paper, we aim to address these limitations by leveraging functional response models (FRM) to develop doubly robust estimators. We demonstrate the performance of our proposed approach using both simulated and real study data. [ABSTRACT FROM AUTHOR]

AbstractIn this article, we propose a class of Lq -norm based U-statistics for a family of global testing problems related to high-dimensional data. This includes testing of mean vector and its spatial sign, simultaneous testing of linear model coefficients, and testing of component-wise independence for high-dimensional observations, among others. Under the null hypothesis, we derive asymptotic normality and independence between Lq -norm based U-statistics for several qs under mild moment and cumulant conditions. A simple combination of two studentized Lq -based test statistics via their p-values is proposed and is shown to attain great power against alternatives of different sparsity. Our work is a substantial extension of He et al. (2021), which is mostly focused on mean and covariance testing, and we manage to provide a general treatment of asymptotic independence of Lq -norm based U-statistics for a wide class of kernels. To alleviate the computation burden, we introduce a variant of the proposed U-statistics by using the monotone indices in the summation, resulting in a U-statistic with asymmetric kernel. A dynamic programming method is introduced to reduce the computational cost from O(nqr) , which is required for the calculation of the full U-statistic, to O(nr) where r is the order of the kernel. Numerical results further corroborate the advantage of the proposed adaptive test as compared to some existing competitors. [ABSTRACT FROM AUTHOR]

This paper is concerned with minimax conditional independence testing. In contrast to some previous works on the topic, which use the total variation distance to separate the null from the alternative, here we use the Wasserstein distance. In addition, we impose Wasserstein smoothness conditions that on bounded domains are weaker than the corresponding total variation smoothness imposed, for instance, by Neykov et al. (2021, Ann. Statist. , 49, 2151–2177). This added flexibility expands the distributions that are allowed under the null and the alternative to include distributions that may contain point masses for instance. We characterize the optimal rate of the critical radius of testing up to logarithmic factors. Our test statistic that nearly achieves the optimal critical radius is novel, and can be thought of as a weighted multi-resolution version of the |$U$| -statistic studied by Neykov et al. (2021, Ann. Statist. , 49, 2151–2177). [ABSTRACT FROM AUTHOR]

High-dimensional parameter testing is commonly used in bioinformatics to analyze complex relationships in gene expression and brain connectivity studies, involving parameters like means, covariances, and correlations. In this paper, we present a novel approach for testing U-statistics-type parameters by leveraging jackknife pseudo-values. Inspired by Tukey's conjecture, we establish the asymptotic independence of these pseudo-values, allowing us to reformulate U-statistics-type parameter testing as a sample mean testing problem. This reformulation enables the use of established sample mean testing frameworks, simplifying the testing procedure. We apply a multiplier bootstrap method to obtain critical values and provide a rigorous theoretical analysis to validate the approach. Simulation studies demonstrate the robustness of our method across a variety of scenarios. Additionally, we apply our approach to investigate differences in the dependency structures of a subset of genes within the Wnt signaling pathway, which is associated with lung cancer. [ABSTRACT FROM AUTHOR]

U-statistics represent a fundamental class of statistics that emerge from modelling quantities of interest defined by multi-subject responses. These statistics generalize the empirical mean of a random variable $ \bf {X} $ X to summations encompassing all distinct k-tuples of observations drawn from $ \bf {X} $ X . A significant advancement was made by Stute [ConditionalU-statistics. Ann. Probab. 19 (1991), pp. 812–825], who introduced conditional U-statistics as a generalization of the Nadaraya–Watson estimates for regression functions. Stute demonstrated their robust pointwise consistency towards the conditional function \[ r^{(k)}(\varphi,\tilde{\bf{t}})=\mathbb{E}\left(\varphi(\bf{Y}_{1},\ldots,\bf{Y}_{k})\,\mid\, (\bf{X}_{1},\ldots,\bf{X}_{k})=\tilde{\bf{t}}\right), \quad\mbox{for}\ \tilde{\bf{t}} \in \mathbb{R}^{pk}, \] r (k) (φ , t ~) = E (φ (Y 1 , ... , Y k) ∣ (X 1 , ... , X k) = t ~) , for t ~ ∈ R pk , where φ is a measurable function. In this investigation, we develop oracle inequalities and upper bounds for kernel-based estimators of conditional U-statistics of general order, applicable across a wide range of metric spaces associated with operators. Our analysis specifically targets doubling measure metric spaces, incorporating a non-negative self-adjoint operator characterized by Gaussian regularity in its heat kernel. Remarkably, our study achieves an optimal convergence rate in certain cases. To derive these results, we explore the regression function within a general framework, introducing several novel insights. These findings are established under sufficiently broad conditions on the underlying distributions. The theoretical results serve as essential tools for advancing the field of general-valued data, with potential applications including the examination of conditional distribution functions, relative-error prediction, the Kendall rank correlation coefficient, and discrimination problems – areas of significant independent interest. [ABSTRACT FROM AUTHOR]

Research objective. The objective of the study was to investigate the impact of virtual laboratories on students' research skills while studying biology in a university environment. Applied research method. The research method used in the study was a research experiment in a virtual laboratory, the method of testing (EETS), and the method of expert evaluation. The statistical analysis was carried out using the Mann-Whitney criterion, Pearson's coefficient, and correlation analysis. The reliability of the method was tested by Cronbach's alpha. Main results. There is a positive correlation between the use of scientific methods and the ability to conduct experiments, as well as the attitude to the learning environment in both the experimental and control groups. The Pearson correlation coefficients were higher for the experimental group; this clearly indicates a stronger connection between their research skills and attitudes toward the learning environment. The ability to process results also has a small positive relationship with attitudes toward the learning environment. Major conclusions. The results of the study demonstrated the positive impact of using virtual laboratories in the study of biological disciplines. [ABSTRACT FROM AUTHOR]

This paper focuses on analysing dependent truncated data. To address this, we draw inspiration from some literatures and employ the Archimedean copula model to establish a correlation between the truncation time and the survival time. Building on this, we refer to the U-statistics and the copula-graphic method to estimate the association parameter and the survival function. Subsequently, we proceed to build a quantile regression model and develop an estimation procedure for the quantile regression parameters using the counting process method. To further validate the efficacy of our approach, we conduct simulation experiments with specific settings of quantiles and correlations. In conclusion, we apply our method to analyse two datasets: one pertaining to HIV transfusion infections and the other related to retirement centres. [ABSTRACT FROM AUTHOR]

Let X 1 , ... , X n be a random sample from the gamma distribution with density f (x) = λ α x α − 1 e − λ x / Γ (α) , x > 0, where both α > 0 (the shape parameter) and λ > 0 (the reciprocal scale parameter) are unknown. The main result shows that the uniformly minimum variance unbiased estimator (UMVUE) of the shape parameter, α, exists if and only if n ≥ 4 ; moreover, it has finite variance if and only if n ≥ 6 . More precisely, the form of the UMVUE is given for all parametric functions α, λ, 1 / α , and 1 / λ . Furthermore, a highly efficient estimating procedure for the two-parameter beta distribution is also given. This is based on a Stein-type covariance identity for the beta distribution, followed by an application of the theory of U-statistics and the delta-method. [ABSTRACT FROM AUTHOR]

We take another look at using Stein's method to establish uniform Berry–Esseen bounds for Studentized nonlinear statistics, highlighting variable censoring and an exponential randomized concentration inequality for a sum of censored variables as the essential tools to carry out the arguments involved. As an important application, we prove a uniform Berry–Esseen bound for Studentized U-statistics in a form that exhibits the dependence on the degree of the kernel. [ABSTRACT FROM AUTHOR]

AbstractWe propose a mean functional that exists for arbitrary probability distributions and characterizes the Pareto distribution within the set of distributions with finite left endpoint. This is in sharp contrast to the mean excess plot, which is meaningless for distributions without an existing mean and has nonstandard behavior when the mean is finite, but the second moment does not exist. The construction of the plot is based on the principle of a single huge jump, which differentiates between distributions with moderately heavy and super heavy tails. We present an estimator of the tail function based on U-statistics and study its large sample properties. Several loss datasets illustrate the use of the new plot. [ABSTRACT FROM AUTHOR]

Deserts and semi-desert countries have become increasingly affected by dust storms in recent years. In this research, the effect of the real-time multivariate of the Madden-Julian Oscillation (MJO) index on the frequency of dust storms in the west of Iran (Sarpol-E-Zahab, Islamabad Gharb, Kermanshah, and Kangavar stations located in Kermanshah province) during February-July for the period 1987-2022 and the frequency percentage of this index for Phases 7-2 (7, 8, 2 and 1) and Phases 3-6 (3, 4, 5 and 6) were investigated. The results of the analysis of the relationship between the MJO and dust storms showed that between 57 and 75% of dust storms occurred in phases 7-2 of the MJO and 25 to 42% in phases 3-6. Phases 7-2 of the MJO have a higher percentage of dust storms than phases 3-6. According to the results of the Mann-Whitney test, the displacement of phases 7-2 and phases 3-6 of the MJO have significantly led to dust storms at the Kermanshah and Kangavar stations. Due to the suitability of the HYSPLIT model for tracking dust storms, the paths of dust entering Kermanshah province were investigated with this model. Tracking the paths of dust entering Kermanshah province with the HYSPLIT model and analyzing the wind speed and direction maps of 850 hPa level indicate an increase in the speed of westerly winds. The increase in the speed of westerly winds and the decrease in soil moisture in phases 7-2 and 3-6 have caused the movement of dust particles from Iraq, eastern parts of Syria, and Khuzestan province to the studied area. [ABSTRACT FROM AUTHOR]

This paper introduces a general semi-parametric method for estimating a vector of parameters in multivariate copula models. The proposed approach uses the moments of the multivariate probability integral random variable to generalize the inversion of Kendall's tau estimator. What makes the new methodology attractive is the fact that it can be performed as soon as one can simulate from the assumed parametric family of copulas. This feature is especially helpful when explicit expressions are not available for the theoretical moments. The consistency and asymptotic normality of the proposed estimators are established under mild conditions. An extensive simulation study indicates that the price to pay for the estimation of the moments is modest and that the new estimators are almost as accurate as the pseudo-maximum likelihood (PML) estimator. The usefulness of the proposed estimators is illustrated on the modelling of multivariate data with copula models where the PML estimator is hardly computable. [ABSTRACT FROM AUTHOR]

Computing cross-partial derivatives using fewer model runs is relevant in modeling, such as stochastic approximation, derivative-based ANOVA, exploring complex models, and active subspaces. This paper introduces surrogates of all the cross-partial derivatives of functions by evaluating such functions at N randomized points and using a set of L constraints. Randomized points rely on independent, central, and symmetric variables. The associated estimators, based on N L model runs, reach the optimal rates of convergence (i.e., O (N − 1) ), and the biases of our approximations do not suffer from the curse of dimensionality for a wide class of functions. Such results are used for (i) computing the main and upper bounds of sensitivity indices, and (ii) deriving emulators of simulators or surrogates of functions thanks to the derivative-based ANOVA. Simulations are presented to show the accuracy of our emulators and estimators of sensitivity indices. The plug-in estimates of indices using the U-statistics of one sample are numerically much stable. [ABSTRACT FROM AUTHOR]

The aim of this paper is to develop a change-point test for functional time series that uses the full functional information and is less sensitive to outliers compared to the classical CUSUM test. For this aim, the Wilcoxon two-sample test is generalized to functional data. To obtain the asymptotic distribution of the test statistic, we prove a limit theorem for a process of U-statistics with values in a Hilbert space under weak dependence. Critical values can be obtained by a newly developed version of the dependent wild bootstrap for non-degenerate 2-sample U-statistics. [ABSTRACT FROM AUTHOR]

Comparison of variability or dispersion of two distributions is the major focus of this work. To this end, we consider a two sample testing problem for detecting dominance in dispersive order and develop a test based on U-statistic approach. We also explore a link between the two measures of variability, viz. dispersive order and Gini's mean difference (GMD). We exploit methodologies based on jackknife empirical likelihood (JEL) and adjusted JEL in order to overcome certain practical difficulties. The performance of the proposed test is assessed by means of a simulation study. Finally, we apply our test in the context of several real life situations including medical studies and insurance data. [ABSTRACT FROM AUTHOR]

We consider the problem of testing a null hypothesis defined by equality and inequality constraints on a statistical parameter. Testing such hypotheses can be challenging because the number of relevant constraints may be on the same order or even larger than the number of observed samples. Moreover, standard distributional approximations may be invalid due to irregularities in the null hypothesis. We propose a general testing methodology that aims to circumvent these difficulties. The constraints are estimated by incomplete U -statistics, and we derive critical values by Gaussian multiplier bootstrap. We show that the bootstrap approximation of incomplete U -statistics is valid for kernels that we call mixed degenerate when the number of combinations used to compute the incomplete U -statistic is of the same order as the sample size. It follows that our test controls type I error even in irregular settings. Furthermore, the bootstrap approximation covers high-dimensional settings making our testing strategy applicable for problems with many constraints. The methodology is applicable, in particular, when the constraints to be tested are polynomials in U-estimable parameters. As an application, we consider goodness-of-fit tests of latent-tree models for multivariate data. [ABSTRACT FROM AUTHOR]

U-statistics represent a fundamental class of statistics used to model quantities derived from responses of multiple subjects. These statistics extend the concept of the empirical mean of a d-variate random variable X by considering sums over all distinct m-tuples of observations of X. Within this realm, W. Stute [134] introduced conditional U-statistics, a generalization of the Nadaraya-Watson estimators for regression functions, and demonstrated their strong point-wise consistency. This paper presented a first theoretical examination of the Dirichlet kernel estimator for conditional U-statistics on the dm-dimensional simplex. This estimator, being an extension of the univariate beta kernel estimator, effectively addressed boundary biases. Our analysis established its asymptotic normality and uniform strong consistency. Additionally, we introduced a beta kernel estimator specifically tailored for conditional U-statistics, demonstrating both weak and strong uniform convergence. Our investigation considered the expansion of compact sets and various sequences of smoothing parameters. For the first time, we examined conditional U-statistics based on mixed categorical and continuous regressors. We presented new findings on conditional U-statistics smoothed by multivariate Bernstein kernels, previously unexplored in the literature. These results are derived under sufficiently broad conditions on the underlying distributions. The main ingredients used in our proof were truncation methods and sharp exponential inequalities tailored to the U-statistics in connection with the empirical processes theory. Our theoretical advancements significantly contributed to the field of asymmetric kernel estimation, with potential applications in areas such as discrimination problems, ℓ-sample conditional U-statistics, and the Kendall rank correlation coefficient. Finally, we conducted some simulations to demonstrate the small sample performances of the estimators. [ABSTRACT FROM AUTHOR]

In the present article, we propose a Jackknife empirical likelihood (JEL) ratio test for testing the independence of time to failure and cause of failure in competing risks data. We use the U-statistics theory to derive the JEL ratio test. The asymptotic distribution of the test statistic is shown to be the standard chi-square distribution. A Monte Carlo simulation study is carried out to assess the finite sample behavior of the proposed test. The performance of the proposed JEL test is compared with the test given by Dewan et al. (2004). Finally, we illustrate our test procedure using two real data sets.

In this work, we study the properties of the cumulative residual entropy generating function (CREGF). We also discuss the non parametric estimation of CREGF. We introduce dynamic cumulative residual entropy generating function (DCREGF). It is shown that the DCREGF determines the distribution uniquely. We study some characterization results using the relationship between DCREGF, hazard rate, and mean residual life function. A new class of life distributions based on decreasing DCREGF is introduced. Finally, we develop a test for decreasing DCREGF and study its performance. [ABSTRACT FROM AUTHOR]

In this paper, a novel test for testing whether data are missing completely at random is proposed. Asymptotic properties of the test are derived utilizing the theory of non-degenerate U-statistics. It is shown that the novel test statistic coincides with the well-known Little's $ d^2 $ d 2 statistic in the case of a multivariate data that has only one variable susceptible to missingness. Then, the extensive simulation study is conducted to examine the performance of the test in terms of the preservation of type I error and in terms of power. Various underlying distributions, dimensions of the data, sample sizes and alternatives are used. Performance of the Little's MCAR test is used as a benchmark for the comparison. The novel test shows better performance in all of the studied scenarios, better preserving the type I error and having higher empirical powers for every studied alternative. [ABSTRACT FROM AUTHOR]

Life categories and probability distributions are part of a new field in reliability that has emerged as a result of the daily generation of data that has become more complex across practical fields. This study demonstrated how well the U-statistics technique can be applied to real-world testing problems, producing more efficient processes that are on par with or even more successful than conventional approaches. Furthermore, there was room for improvement in the performance of these methods. An approach tending toward normalcy was supported by comparing a unique U-statistic test with the used better than age in moment generating ordering (UBAmgf) test statistic, In this manuscript, a novel nonparametric technique has been developed to test the belonging of a dataset to a distribution of a new statistical class survival function, the moment generating function for used better than aged (UBAmgf). This type of test was crucial in practical life, such as implementing a specific strategy of proposed therapy for a particular disease, deeming it futile if the survival data was exponential (accepting H0) (the suggested therapeutic approach does not exhibit positive or negative effects on the patients). Once the survival data was UBAmgf, the treatment or device or system employed yields an expected overall current value better or higher than the older device governed by the asymptotic survival function (discussed in the Applications section). The appropriateness of the proposed statistical test's application range was properly determined by calculating its test efficiency and critical values and comparing them with other tests, whether in complete or censored data. Finally, we applied this proposed test technique in the manuscript to a different set of real data in both cases. [ABSTRACT FROM AUTHOR]

Abstract.To check the significance of the regression coefficients in the linear component of high-dimensional partial linear models, we proposed some projection-based test statistics. These test statistics are connected with U-statistics of order two and they are applicable for diverging dimensions and heteroscedastic model errors. By using the martingale central limit theorem, we show the asymptotic normalities of the proposed test statistics under the null hypothesis and local alternative hypotheses. The performance of test statistics are evaluated by simulation studies. The simulation results show that the proposed test statistics are powerful and have the correct type-I error asymptotically under the null hypothesis. [ABSTRACT FROM AUTHOR]

U‐statistics constitute a large class of estimators, generalizing the empirical mean of a random variable X$$ \mathbf{X} $$ to sums over every k$$ k $$‐tuple of distinct observations of X$$ \mathbf{X} $$. They may be used to estimate a regular functional θ(ℙX)$$ \theta \left({\mathbb{P}}_{\mathbf{X}}\right) $$ of the law of X$$ \mathbf{X} $$. When a vector of covariates Z$$ \mathbf{Z} $$ is available, a conditional U‐statistic describes the effect of z$$ \mathbf{z} $$ on the conditional law of X$$ \mathbf{X} $$ given Z=z$$ \mathbf{Z}=\mathbf{z} $$, by estimating a regular conditional functional θ(ℙX|Z=·)$$ \theta \left({\mathbb{P}}_{\mathbf{X}\mid \mathbf{Z}=\cdotp}\right) $$. We state nonasymptotic bounds of general conditional U‐statistics and study their asymptotics too. Assuming a parametric model of the conditional functional of interest, we propose a regression‐type estimator based on conditional U‐statistics. Its theoretical properties are derived, first in a nonasymptotic framework and then in two different asymptotic regimes. Some examples are given to illustrate our methods. [ABSTRACT FROM AUTHOR]

This paper analyzes several covariance matrix U‐tests, which are constructed by modifying the classical John‐Nagao and Ledoit‐Wolf tests, under the elliptically distributed data structure. We study the limiting distributions of these location‐invariant test statistics as the data dimension p$$ p $$ may go to infinity in an arbitrary way as the sample size n$$ n $$ does. We find that they tend to have unsatisfactory size performances for general elliptical population. This is mainly because such population often possesses high‐order correlations among their coordinates. Taking such kind of dependency into consideration, we propose necessary corrections for these tests to cope with elliptically high‐dimensional data. For computational efficiency, alternative forms of the new test statistics are also provided. We derive the universal (n,p)$$ \left(n,p\right) $$ asymptotic null distributions of the proposed test statistics under elliptical distributions and beyond. The powers of the proposed tests are further investigated. The accuracy of the tests is demonstrated by simulations and an empirical study. [ABSTRACT FROM AUTHOR]

Stute (1991) introduced a class of so-called conditional U-statistics, which may be viewed as a generalization of the Nadaraya-Watson estimates of a regression function. Stute proved their strong pointwise consistency to: r (k) (φ , t) : = E [ φ (Y 1 , ... , Y k) | (X 1 , ... , X k) = t ] , for t ∈ R d k. This article deals with a quite general non parametric statistical curve estimation setting including the Stute estimator as a particular case. The class of "delta sequence estimators" is defined and treated here. This class includes also the orthogonal series and histogram methods. The theoretical results concerning the exponential inequalities and the asymptotic normality, established in this article, are (or will be) key tools for many further developments in functional estimation. As a by-product of our proofs, we state consistency results for the delta sequences conditional U-statistics estimator, under the random censoring. Potential applications include discrimination problems, metric learning and multipartite ranking, Kendall rank correlation coefficient, generalized U-statistics, and set indexed conditional U-statistics. [ABSTRACT FROM AUTHOR]

Aims: Dental procedures involve intricate techniques that can be challenging to visualize, often hindering imitation and assessment. In this study, the impression-taking performance of abutment teeth was quantitatively analyzed to create objective indexes for dental skill education. Methods: Participants were divided into two groups of different clinical experience levels: 10 dentists and 10 dental students. An aluminum model of abutment teeth was employed to simplify the experiment. An optical motion capture system (VICON, Oxford, UK) measured participants’ movements. The impression accuracy, time length on the analyzed section, impression material pouring speed, total amount of impression material used, and syringe tip trajectory were evaluated. Fisher’s exact test and Mann-Whitney U test were used to compare the two groups’ results (α=0.05). Results: In the dentist group, there were few apparent failures and a high impression accuracy. The amount of impression material dispensed tended to be larger in the dentist group, with longer practice time and slower syringe movement speed. This suggested that the inexperienced participants were sufficiently unable to pour out the impression material. The syringe tip trajectories were not significantly different between the groups. An instructor’s advice is often limited to abstract feedback; therefore, specific suggestions might assist in effective skill education. Conclusion: It is possible to quantitatively analyze impression-taking performance and provide helpful information for dental skill education by using this system. [ABSTRACT FROM AUTHOR]

In this paper, we study the asymptotic behavior of specification tests in conditional moment restriction models under first‐order local identification failure with dependent data. More specifically, we obtain conditions under which the conventional specification test for conditional moment restrictions retains its standard normal limit when first‐order local identification fails but global identification is still attainable. In the process, we derive some novel intermediate results that include extending the first‐ and second‐order local identification framework to models defined by conditional moment restrictions, establishing the rate of convergence of the GMM estimator and characterizing the asymptotic representation for degenerate U‐statistics under strong mixing dependence. Importantly, the specification test is robust to first‐order local identification failure regardless of the number of directions in which the Jacobian of the conditional moment restrictions is degenerate and remains valid even if the model is first‐order identified. [ABSTRACT FROM AUTHOR]

The main aim of this study was to compare goal scoring patterns between the two most recent FIFA World CupTM (WC) tournaments: Russia 2018 and Qatar 2022. Match performance data were extracted using the ProVision database (StatsPerform, Chicago, USA). Variables used to analyse goals (not including penalty shootout goals) included the match period in which these were scored, the type of action and different types of play, body part used, defensive pressure, possession duration and expected goals (xG) values. A Chi-square test was used to compare qualitative variables across competitions while quantitative variables were compared using a nonparametric Mann-Whitney U-test for independent samples. Altogether, 169 goals were scored in WC 2018 vs. 172 goals in WC 2022. No differences occurred across competitions for the period in which goals were scored. In both tournaments the majority was scored in the second-half and towards the end of play. Significant differences were observed for the type of action, type of play and body part used prior to scoring a goal (p < .05). These differences can be explained by the record number of own goals and goals scored from set-pieces in 2018 and an increase in goals scored from open-play (from positional attacks notably) in 2022. Analysis of open-play situations showed that teams recorded a higher xG value and converted more of their chances (xG = 122.8 vs. 128 goals, xG difference = +5.2) in 2022 thus were more efficient compared with 2018. In sum, goal scoring patterns largely differed between the two most recent World Cup tournaments. [ABSTRACT FROM AUTHOR]

The mounting generation has been struggling from a lack of understanding and assistance regarding sex since everyone desires a fantastic sex life, which is incorrectly portrayed in pornographic films, resulting in sexual anxiety, an important hindrance to an individual's sexual satisfaction. Sexual anxiety involves feelings of fear, trepidation, and worry about sexual activities or performances; it can also perpetuate a detrimental cycle in which people become paranoid about sexual performance and are afraid of unsatisfactory experiences and future performance. This study aims to delve into the complex realm of sexual anxiety among unmarried young adults and gender differences. The data was acquired through Google Forms. The sample comprises 138 unmarried individuals (55 male & 83 female). The instrument utilized in the study was the Sexual Anxiety Scale (SAS) by Pramod. In the present study, descriptive statistics and the Mann-Whitney U test were employed using a statistical package for the social sciences (SPSS). The findings reveal that 16.67% of the sample have high levels of sexual anxiety. Results of the Mann-Whitney U Test indicated a statistically significant difference in sexual anxiety levels between men and women. 21.69% of women experience high sexual anxiety which is higher than men who experience 9.08% of sexual anxiety which illuminates a pronounced disparity that reveals that women experience higher levels of sexual anxiety than men. The study also defines the limitations and future implications of the study. Understanding the factors causing higher sexual anxiety in women is crucial for developing tailored interventions and support mechanisms to address these nuanced needs of individual and socio-cultural factors. With the help of this, it may be possible to reduce the burden of sexual anxiety among women, improve their sexual well-being, and promote gender equality in sexual health and satisfaction. It also contributes to curriculum development and fostering a healthy attitude towards sex education. [ABSTRACT FROM AUTHOR]

Suppose that a sequence of random pairs (X 1 , Y 1) , ... , (X n , Y n) is subject to a gradual change in the sense that for K 1 ≤ K 2 ∈ { 1 , ... , n } , the joint distribution is F before K 1 , G after K 2 , and gradually moving from F to G between the two times of change K 1 and K 2 . This setup elegantly generalizes the abrupt-change model that is usually assumed in the change-point analysis. Under this configuration, asymptotically unbiased estimates of Kendall's tau up to and after the change are proposed, as well as tests and estimators of change points related to these measures. The asymptotic behaviour of the introduced estimators and test statistics is rigorously investigated, in particular by demonstrating a general result on weighted indexed U-statistics computed under a heterogeneous pattern. A simulation study is conducted to examine the sampling properties of the proposed methods under different scenarios of change in the dependence structure of bivariate series. An illustration is given on a time series of monthly atmospheric carbon dioxide concentrations and global temperature for the period 1959–2015. [ABSTRACT FROM AUTHOR]

The convergence of a sequence of point processes with dependent points, defined by a symmetric function of iid high-dimensional random vectors, to a Poisson random measure is proved. This also implies the convergence of the joint distribution of a fixed number of upper order statistics. As applications of the result a generalization of maximum convergence to point process convergence is given for simple linear rank statistics, rank-type U-statistics and the entries of sample covariance matrices. [ABSTRACT FROM AUTHOR]

We consider the problem of detecting distributional changes in a sequence of high dimensional data. Our approach combines two separate statistics stemming from L p norms whose behavior is similar under H 0 but potentially different under H A , leading to a testing procedure that that is flexible against a variety of alternatives. We establish the asymptotic distribution of our proposed test statistics separately in cases of weakly dependent and strongly dependent coordinates as min { N , d } → ∞ , where N denotes sample size and d is the dimension, and establish consistency of testing and estimation procedures in high dimensions under one-change alternative settings. Computational studies in single and multiple change point scenarios demonstrate our method can outperform other nonparametric approaches in the literature for certain alternatives in high dimensions. We illustrate our approach through an application to Twitter data concerning the mentions of U.S. governors. [ABSTRACT FROM AUTHOR]

In recent years, there has been a notable shift in focus towards the analysis of non-stationary time series, driven largely by the complexities associated with delineating significant asymptotic behaviors inherent to such processes. The genesis of the theory of locally stationary processes arises from the quest for asymptotic inference grounded in nonparametric statistics. This paper endeavors to formulate a comprehensive framework for conducting inference within the realm of locally stationary functional time series by harnessing the conditional U-statistics methodology as propounded by W. Stute in 1991. The proposed methodology extends the Nadaraya-Watson regression function estimations. Within this context, a novel estimator was introduced for the single index conditional Ustatistics operator, adept at accommodating the non-stationary attributes inherent to the data-generating process. The primary objective of this paper was to establish the weak convergence of conditional Uprocesses within the domain of locally stationary functional mixing data. Specifically, the investigation delved into scenarios of weak convergence involving functional explanatory variables, considering both bounded and unbounded sets of functions while adhering to specific moment requirements. The derived findings emanate from broad structural specifications applicable to the class of functions and models under scrutiny. The theoretical insights expounded in this study constitute pivotal tools for advancing the domain of functional data analysis. [ABSTRACT FROM AUTHOR]

Background: The impact of a chronic disease on the health of an individual is reflected by the different aspects of quality of life. The aim of this paper is to assess the impact of celiac disease in adolescents on their quality of life in four subscales: dysphoria, limitations, health concerns, and undertreatment due to gender differences. Methodology: Data collection took place from 04/2019 to 05/2020 in adolescents aged 15-18 years attending gastroenterology outpatient clinics in DFN Košice. A total of 33 patients (16 boys, 17 girls) completed the standardized questionnaire for patients with celiac disease – CD-QOL. The mean age of the adolescents was 16.36 ± 1.11 and the mean duration of their treatment was 8.39 ± 5.04 years. Data were analyzed by descriptive statistics and Mann-Whitney U test. Results: No statistically significant differences were confirmed in adolescents with celiac disease with respect to gender differences in the four domains studied. Boys and girls had statistically significantly different overall quality of life scores (U = 81.50, p = 0.049). Conclusion: Quality of life assessment is important for healthcare providers, caregivers, but especially for patients. Early detection of determinants that modify life with celiac disease can be the basis for the preparation, plan and implementation of interventions to benefit the health and overall well-being of individuals with celiac disease. [ABSTRACT FROM AUTHOR]

With our increased ability to capture large data, causal inference has received renewed attention and is playing an ever-important role in biomedicine and economics. However, one major methodological hurdle is that existing methods rely on many unverifiable model assumptions. Thus robust modeling is a critically important approach complementary to sensitivity analysis, where it compares results under various model assumptions. The more robust a method is with respect to model assumptions, the more worthy it is. The doubly robust estimator (DRE) is a significant advance in this direction. However, in practice, many outcome measures are functionals of multiple distributions, and so are the associated estimands, which can only be estimated via U-statistics. Thus most existing DREs do not apply. This article proposes a broad class of highly robust U-statistic estimators (HREs), which use semiparametric specifications for both the propensity score and outcome models in constructing the U-statistic. Thus, the HRE is more robust than the existing DREs. We derive comprehensive asymptotic properties of the proposed estimators and perform extensive simulation studies to evaluate their finite sample performance and compare them with the corresponding parametric U-statistics and the naive estimators, which show significant advantages. Then we apply the method to analyze a clinical trial from the AIDS Clinical Trials Group. [ABSTRACT FROM AUTHOR]

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Background: Autism Spectrum Disorder (ASD) is a neurodevelopmental condition with unique differences in social interaction, communication, and a spectrum of behavioral characteristics. In the past, motor disturbance in individuals with ASD has not been considered a significant core deficit due to the predominant focus on sociability and communication issues. However, recent studies indicate that motor deficits are indeed associated with the fundamental symptoms of ASD. As there is limited research on the motor behavior of children with ASD, particularly in China, the objective of this study is to investigate the development of fundamental movement skills (FMS) in children with ASD and compare them to typically developing children. Method: The study recruited 108 children with ASD (87 boys, 21 girls) aged 7-10 years from two special education rehabilitation centers in Wuhan, China. For comparison, a control group of 108 typically developing children, matched by age and gender, was randomly selected from three local primary schools. FMS were assessed using the Movement Assessment Battery for Children - Second Edition (MABC-2), which evaluates manual dexterity, aiming and catching, as well as static and dynamic balance. Group differences on MABC-2 percentile scores were analyzed using descriptive statistics and Mann-Whitney U test. Effect sizes were also calculated for practical significance. Results: Findings from the study showed that a significant majority, around 80%, of children with ASD either displayed motor challenges or were at risk of developing such delays. When comparing to their typically developing peers, children with ASD scored notably lower in areas of manual dexterity, ball skills, and both static and dynamic balance (with all these findings being statistically significant at p < 0.001). Interestingly, gender did not show a significant influence on these results (p > 0.05). Conclusion: In addition to addressing the other skill development areas outlined in the diagnostic manual for ASD, clinicians diagnosing and treating children with ASD should also assess the presence of motor skill development. For individuals with ASD who have co-existing motor difficulties, it is essential to offer evidence-based interventions tailored to their specific needs. [ABSTRACT FROM AUTHOR]

We derive limiting distributions of symmetrized estimators of scatter. Instead of considering all n (n - 1) / 2 pairs of the n observations, we only use nd suitably chosen pairs, where d ≥ 1 is substantially smaller than n. It turns out that the resulting estimators are asymptotically equivalent to the original one whenever d = d (n) → ∞ at arbitrarily slow speed. We also investigate the asymptotic properties for arbitrary fixed d. These considerations and numerical examples indicate that for practical purposes, moderate fixed values of d between 10 and 20 yield already estimators which are computationally feasible and rather close to the original ones. [ABSTRACT FROM AUTHOR]

Recent studies have emphasized the connection between machine learning feature importance measures and total order sensitivity indices (total effects, henceforth). Feature correlations and the need to avoid unrestricted permutations make the estimation of these indices challenging. Additionally, there is no established theory or approach for non-Cartesian domains. We propose four alternative strategies for computing total effects that account for both dependent and constrained features. Our first approach involves a generalized winding stairs design combined with the Knothe-Rosenblatt transformation. This approach, while applicable to a wide family of input dependencies, becomes impractical when inputs are physically constrained. Our second approach is a U-statistic that combines the Jansen estimator with a weighting factor. The U-statistic framework allows the derivation of a central limit theorem for this estimator. However, this design is computationally intensive. Then, our third approach uses derangements to significantly reduce computational burden. We prove consistency and central limit theorems for these estimators as well. Our fourth approach is based on a nearest-neighbour intuition and it further reduces computational burden. We test these estimators through a series of increasingly complex computational experiments with features constrained on compact and connected domains (circle, simplex), non-compact and non-connected domains (Sierpinski gaskets), we provide comparisons with machine learning approaches and conclude with an application to a realistic simulator. [ABSTRACT FROM AUTHOR]