Composite hypothesis testing using summary statistics is a well-established approach for assessing the effect of a single marker or gene across multiple traits or omics levels. Numerous procedures have been developed for this task and have been successfully applied to identify complex patterns of association between traits, conditions, or phenotypes. However, existing methods often struggle with scalability in large datasets or fail to account for dependencies between traits or omics levels, limiting their ability to control false positives effectively. To overcome these challenges, we present the qch_copula approach, which integrates mixture models with a copula function to capture dependencies between traits or omics and provides rigorously defined P-values for any composite hypothesis. Through a comprehensive benchmark against eight state-of-the-art methods, we demonstrate that qch_copula controls Type I error rates effectively while enhancing the detection of joint association patterns. Compared to other mixture model-based approaches, our method notably reduces memory usage during the EM algorithm, allowing the analysis of up to 20 traits and 105−106 markers. The effectiveness of qch_copula is further validated through two application cases in human and plant genetics. The method is available in the R package qch, accessible on CRAN.

The purpose of this research is to determine and analyze the influence of Promotion, Service Quality, and Product Quality on Customer Loyalty for beverages at the Haus! outlet in Depok, with Customer Satisfaction as an intervening variable. The sample for this research consists of customers who have purchased Haus! beverages in Depok and reside in Depok. The sampling technique used the Lemeshow formula. The research sample consisted of 150 respondents, and the data collection method employed a questionnaire instrument. The method used is Partial Least Square with the help of SmartPLS 3.0 software, including Convergent Validity Test, Discriminant Validity, Average Variance Extracted (AVE), Composite Reliability Test, R-Square Test, Hypothesis Test, Path Coefficient, and Specific Indirect Effect. The Path Coefficient test results show that Promotion, Service Quality, and Product Quality have an impact on Customer Satisfaction. Service Quality and Product Quality affect Customer Loyalty. However, Promotion does not affect Customer Loyalty. The results of the Specific Indirect Effect test show that Promotion, Service Quality, and Product Quality affect Customer Loyalty through Customer Satisfaction.

BackgroundMultiple testing of composite null hypotheses is critical for identifying simultaneous signals across studies. While it is common to incorporate external information in simple null hypotheses, exploiting such auxiliary covariates to provide prior structural relationships among composite null hypotheses and boost the statistical power remains challenging.ResultsWe propose a robust and powerful covariate-assisted composite null hypothesis testing (CoCoNuT) procedure based on a Bayesian framework to identify replicable signals in two studies while asymptotically controlling the false discovery rate. CoCoNuT innovatively adopts a three-dimensional mixture model to consider two primary studies and an integrative auxiliary covariate jointly. While accounting for heterogeneity across studies, the local false discovery rate optimally captures cross-study and cross-feature information, providing improved rankings of feature importance.ConclusionsTheoretical and empirical evaluations confirm the validity and efficiency of CoCoNuT. Extensive simulations demonstrate that CoCoNuT outperforms conventional methods that do not exploit auxiliary covariates while controlling the FDR. We apply CoCoNuT to schizophrenia genome-wide association studies, illustrating its higher power in identifying replicable genetic variants with the assistance of relevant auxiliary studies.

To verify the adequacy of the constructed models of distribution laws of random variables, various nonparametric goodness-of-fit tests are usually used, in particular, Kolmogorov, Kramer – Mises – Smirnov, Anderson – Darling, Kuiper, and Watson. When a simple hypothesis is tested, nonparametric goodness-of-fit tests are “distribution-free”: the asymptotic distributions of statistics do not depend on the type of law against which the hypothesis is tested. When testing composite hypotheses, when the parameters of the assumed law are estimated from a sample, the property of “freedom from distribution” is lost, and the distributions of statistics become dependent on a number of factors. In such situations, the use of nonparametric goodness-of-fit tests is possible only with the support of appropriate software that allows the achieved significance level Pv to be assessed using simulation modeling. The distributions of the statistics of the Zhang tests, which are a development of the Kolmogorov, Kramer – Mises – Smirnov, and Anderson – Darling tests, respectively, depend on the sample sizes, so their wide application in testing simple and complex hypotheses is possible only with the support of the Monte Carlo method. Distributions of goodness-of-fit tests statistics (when testing simple and composite hypotheses) can vary significantly due to the natural presence of rounding errors. A signal about the possibility of such a situation is the presence of a significant number of repeating values in the analyzed samples. In such situations, making a decision on the results of the inspection is also impossible without the use of simulation modeling. In recent years, several criteria have been proposed, aimed, for example, at checking whether samples belong to a normal or uniform law, the statistics of which are based on various entropy estimates. As experience shows, with respect to some competing hypotheses, such criteria demonstrate higher power estimates compared to classical nonparametric goodness-of-fit tests. When constructing the statistics of the Noughabi test to distinguish between two hypotheses, the Kullback-Leibler divergence was used, and the estimate proposed by Vasicek was taken as an estimate of entropy. This paper shows how the distributions of the Noughabi test statistics depend on the sample size n and the window size m, and how the distributions of the test statistics change when testing various composite hypotheses. The power of the criterion in testing norma-lity against various competing hypotheses was investigated. It is shown how, for given n, the power depends on the size of the “window” m. The existence of an optimal m is shown, at which the power is maximum relative to the competing hypothesis under consideration. It is shown that for a given n, the optimal values of m, as a rule, do not coincide for different competing hypotheses. Obviously, the application of such criteria in practice also implies the use of appropriate software and simulation modeling.

Testing simple or composite hypothesis on a functional parameter has attracted considerable attention in time series analysis. To accommodate for the unknown temporal dependence, classical nonparametric approaches such as block bootstrapping and subsampling all involve a bandwidth parameter, the choice of which can substantially affect the finite sample performance. The self normalization (SN) method is tuning parameter free when applied to the inference of a finite-dimensional parameter but its applicability to a functional parameter is unknown. In this article, we propose a sample splitting based approach to generalize the SN method to hypothesis testing of a functional parameter. Our SS-SN (sample splitting plus self-normalization) idea is broadly applicable to many testing problems for functional parameters, including testing for simple/composite hypothesis on marginal cumulative distribution function, testing for time-reversibility and testing for a change point on the spectral distribution of a multivariate time series. Specifically, we derive the pivotal limiting distributions of our SS-SN test statistics under the null for both simple and composite null hypothesis, and derive the limiting power function under the local alternatives. Numerical simulations show that our new tests tend to yield accurate size with competitive power performance as compared to many existing ones. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Intersection and Union of Subspaces With Applications to Communication Over Authenticated Classical-Quantum Channels and Composite Hypothesis Testing

Summary Heteroskedasticity poses several methodological challenges in designing valid and powerful procedures for simultaneous testing of composite null hypotheses. In particular, the conventional practice of standardizing or rescaling heteroskedastic test statistics in this setting may severely affect the power of the underlying multiple testing procedure. Additionally, when the inferential parameter of interest is correlated with the variance of the test statistic, methods that ignore this dependence may fail to control the Type I error at the desired level. We propose a new heteroskedasticity-adjusted multiple testing procedure that avoids data reduction by standardization and directly incorporates the side information from the variances into the testing procedure. Our approach relies on an improved nonparametric empirical Bayes deconvolution estimator that offers a practical way of capturing the dependence between the inferential parameter of interest and the variance of the test statistic. We develop theory to establish that the proposed procedure is asymptotically valid and optimal for false discovery rate control. Simulation results demonstrate that our method outperforms existing procedures, with substantial power gains across many settings at the same false discovery rate level. The method is illustrated with an application involving the detection of engaged users on a mobile game app.

Large-scale mediation analysis has received increasing interest in recent years, especially in genome-wide epigenetic studies. The statistical problem in large-scale mediation analysis concerns testing composite null hypotheses in the context of large-scale multiple testing. The classical Sobel's and joint significance tests are overly conservative and therefore are underpowered in practice. In this work, we propose a testing method for large-scale composite null hypothesis testing to properly control the type I error and hence improve the testing power. Our method is simple and essentially only requires counting the number of observed test statistics in a certain region. Non-asymptotic theories are established under weak assumptions and indicate that the proposed method controls the type I error well and is powerful. Extensive simulation studies confirm our non-asymptotic theories and show that the proposed method controls the type I error in all settings and has strong power. A data analysis on DNA methylation is also presented to illustrate our method.

Work extraction is one of the most central processes in quantum thermodynamics. However, the prior analysis of optimal extractable work has been restricted to a limited operational scenario where complete information about the initial state is given. Here, we introduce a general framework of black box work extraction, which addresses the inaccessibility of information on the initial state. We show that the optimal extractable work in the black box setting is completely characterized by the performance of a composite hypothesis testing task, a fundamental problem in information theory. We employ this general relation to reduce the asymptotic black box work extraction to the quantum Stein's lemma in composite hypothesis testing, allowing us to provide their exact characterization in terms of the Helmholtz free energy. We also show a new quantum Stein's lemma motivated in this physical setting, where a composite hypothesis contains a certain correlation. Our work exhibits the importance of information about the initial state and gives a new interpretation of the quantities in the composite quantum hypothesis testing, encouraging the interplay between the physical settings and the information theory.

Improved PHY-layer authentication utilizing multi-modal features for mmWave MIMO UAV-enabled systems

On the use of the cumulant generating function for inference on time series

Spectrum sensing in uncalibrated MIMO-based cognitive radios

The problem of testing composite hypotheses with respect to the equal parameters of a normal distribution using the constrained Bayesian method is discussed. Hypotheses are tested using the maximum likelihood and Stein’s methods. The optimality of our decision rule is shown by the following criteria: the mixed directional false discovery rate, the false discovery rate, and the Type I and Type II errors, under the conditions of providing a desired level of constraint. The algorithms for implementing the proposed methods and the computational tools for their application are included. Simulation results show validity of the theoretical results along with their superiority over the classical Bayesian method.

Mediation analysis aims to assess if, and how, a certain exposure influences an outcome of interest through intermediate variables. This problem has recently gained a surge of attention due to the tremendous need for such analyses in scientific fields. Testing for the mediation effect (ME) is greatly challenged by the fact that the underlying null hypothesis (i.e. the absence of MEs) is composite. Most existing mediation tests are overly conservative and thus underpowered. To overcome this significant methodological hurdle, we develop an adaptive bootstrap testing framework that can accommodate different types of composite null hypotheses in the mediation pathway analysis. Applied to the product of coefficients test and the joint significance test, our adaptive testing procedures provide type I error control under the composite null, resulting in much improved statistical power compared to existing tests. Both theoretical properties and numerical examples of the proposed methodology are discussed.

Dealing with censored data is an important concern in reliability and survival analysis. Non-destructive one-shot devices are an extreme case of interval censoring, wherein we only know if a device has failed or not before an inspection time. Besides, non-destructive one-shot devices are frequently highly reliable with large lifetimes, and then long experimentation times would be needed for inference under normal operating conditions. Alternatively, accelerated life tests (ALTs) shorten the lifetime of the devices by increasing one or more stress factors causing failure. Then, after suitable inference, results can be extrapolated to normal conditions. In particular, step-stress ALT designs increase the stress level at which devices are tested throughout the experiment at some fixed times. Under the non-destructive one-shot device set-up, the number of failures is recorded at some inspection times, including the times of stress change, then resulting in censored data. Among the most popular lifetime distributions used to analyze survival data, the lognormal distribution has hazard function with an increasing–decreasing behavior, which is encountered often in practice as units usually experience early failure and then stabilize over time in terms of performance. However, the classical maximum likelihood estimator (MLE) of parameters of the lognormal lifetime distribution may get highly influenced by data contamination. In this paper we propose a family of divergence-based robust estimators for non-destructive one-shot device step-stress experiments under the lognormal lifetime distribution. Further, from the robust estimators, a generalization of the popular Wald-type test statistic based on the MLE for testing composite null hypothesis is defined, resulting in a robust divergence-based family of test statistics.

This paper addresses jamming attack detection issue in a millimeter Wave (mmWave) massive MIMO system under noise uncertainty. Specifically, we apply the generalized likelihood ratio test (GLRT) to develop a one-step GLRT scheme for detecting jamming attack under the homogeneous and partially homogeneous noise environments, and exploit training data to estimate the unknown noise statistical information and replace it with resulting estimation in deriving GLRT procedure to obtain adaptive GLRT detection scheme. We also design a two-step GLRT scheme, where we first assume the unknown noise statistical information is known, and derive GLRT based on test data, and then replace it by the sample covariance matrix based on training data only to achieve a fully adaptive jamming attack detector. With the help of statistical signal subspace analysis and composite hypothesis testing theories, we further examine the statistical distributions of the jamming attack detection schemes and present the closed-form expressions of false alarm and detection probabilities for the proposed schemes under different noise environments. Finally, we implement extensive simulations to validate the theoretical results and evaluate the detection efficiency under various parameters.

The problem of adaptive radar detection with a polarimetric Frequency Diverse Array Multiple-Input Multiple-Output (FDA-MIMO) radar is addressed in this paper. At the design stage, the target detection problem is formulated as a composite hypothesis test, with the unknowns given by the target angle, incremental range (target displacement with respect to the center of the occupied range cell), and scattering matrix, as well as the interference covariance matrix. The formulated detection problem is handled by resorting to sub-optimal design strategies based on the Generalized Likelihood Ratio (GLR) criterion. The resulting detectors demand, under the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\mathrm{{1}}$</tex-math></inline-formula> hypothesis, the solution of a box-constrained optimization problem for which several iterative techniques, i.e., the Linearized Array Manifold (LAM), the Gradient Projection Method (GPM), and the Coordinate Descent (CD) algorithms, are exploited. At the analysis stage, the performance of the proposed architectures, which ensure the bounded CFAR property, is evaluated via Monte Carlo simulations and compared with the benchmarks in both white and colored disturbance.

In this paper, we introduce the restricted minimum density power divergence Gaussian estimator (MDPDGE) and study its main asymptotic properties. In addition, we examine it robustness through its influence function analysis. Restricted estimators are required in many practical situations, such as testing composite null hypotheses, and we provide in this case constrained estimators to inherent restrictions of the underlying distribution. Furthermore, we derive robust Rao-type test statistics based on the MDPDGE for testing a simple null hypothesis, and we deduce explicit expressions for some main important distributions. Finally, we empirically evaluate the efficiency and robustness of the method through a simulation study.

BackgroundA greatly growing body of literature has revealed the mediating role of DNA methylation in the influence path from childhood maltreatment to psychiatric disorders such as post-traumatic stress disorder (PTSD) in adult. However, the statistical method is challenging and powerful mediation analyses regarding this issue are lacking.MethodsTo study how the maltreatment in childhood alters long-lasting DNA methylation changes which further affect PTSD in adult, we here carried out a gene-based mediation analysis from a perspective of composite null hypothesis in the Grady Trauma Project (352 participants and 16,565 genes) with childhood maltreatment as exposure, multiple DNA methylation sites as mediators, and PTSD or its relevant scores as outcome. We effectively addressed the challenging issue of gene-based mediation analysis by taking its composite null hypothesis testing nature into consideration and fitting a weighted test statistic.ResultsWe discovered that childhood maltreatment could substantially affected PTSD or PTSD-related scores, and that childhood maltreatment was associated with DNA methylation which further had significant roles in PTSD and these scores. Furthermore, using the proposed mediation method, we identified multiple genes within which DNA methylation sites exhibited mediating roles in the influence path from childhood maltreatment to PTSD-relevant scores in adult, with 13 for Beck Depression Inventory and 6 for modified PTSD Symptom Scale, respectively.ConclusionOur results have the potential to confer meaningful insights into the biological mechanism for the impact of early adverse experience on adult diseases; and our proposed mediation methods can be applied to other similar analysis settings.

High-throughput technologies have made high-dimensional settings increasingly common, providing opportunities for the development of high-dimensional mediation methods. We aimed to provide useful guidance for researchers using high-dimensional mediation analysis and ideas for biostatisticians to develop it by summarizing and discussing recent advances in high-dimensional mediation analysis. The method still faces many challenges when extended single and multiple mediation analyses to high-dimensional settings. The development of high-dimensional mediation methods attempts to address these issues, such as screening true mediators, estimating mediation effects by variable selection, reducing the mediation dimension to resolve correlations between variables, and utilizing composite null hypothesis testing to test them. Although these problems regarding high-dimensional mediation have been solved to some extent, some challenges remain. First, the correlation between mediators are rarely considered when the variables are selected for mediation. Second, downscaling without incorporating prior biological knowledge makes the results difficult to interpret. In addition, a method of sensitivity analysis for the strict sequential ignorability assumption in high-dimensional mediation analysis is still lacking. An analyst needs to consider the applicability of each method when utilizing them, while a biostatistician could consider extensions and improvements in the methodology.