Proposed Test Statistic Research Articles

Structured testing of genetic association with mixed clinical outcomes.

Genetic factors play a fundamental role in disease development. Studying the genetic association with clinical outcomes is critical for understanding disease biology and devising novel treatment targets. However, the frequencies of genetic variations are often low, making it difficult to examine the variants one-by-one. Moreover, the clinical outcomes are complex, including patients' survival time and other binary or continuous outcomes such as recurrences and lymph node count, and how to effectively analyze genetic association with these outcomes remains unclear. In this article, we proposed a structured test statistic for testing genetic association with mixed types of survival, binary, and continuous outcomes. The structured testing incorporates known biological information of variants while allowing for their heterogeneous effects and is a powerful strategy for analyzing infrequent genetic factors. Simulation studies show that the proposed test statistic has correct type I error and is highly effective in detecting significant genetic variants. We applied our approach to a uterine corpus endometrial carcinoma study and identified several genetic pathways associated with the clinical outcomes.

Nonparametric tests for combined location-scale and Lehmann alternatives using adaptive approach and max-type metric

The paper deals with the classical two-sample problem for the combined location-scale and Lehmann alternatives, known as the versatile alternative. Recently, a combination of the square of the standardized Wilcoxon, the standardized Ansari–Bradley and the standardized Anti-Savage statistics based on the Euclidean distance has been proposed. The Anti-Savage test is the locally most powerful rank test for the right-skewed Gumbel distribution. Furthermore, the Savage test is the locally most powerful linear rank test for the left-skewed Gumbel distribution. Then, a test statistic combining the Wilcoxon, the Ansari–Bradley, and Savage statistics is proposed. The limiting distribution of the proposed statistic is derived under the null and the alternative hypotheses. In addition, the asymptotic power of the suggested statistic is investigated. Moreover, an adaptive test is proposed based on a selection rule. We compare the power performance against various fixed alternatives using Monte Carlo. The proposed test statistic displays outstanding performance in certain situations. An illustration of the proposed test statistic is presented to explain a biomedical experiment. Finally, we offer some concluding remarks.

Testing Homoskedasticity in Spatial Panel Data Models

A robust test statistic for testing homoskedasticity in spatial panel data models that have entity and time fixed effects is introduced in a quasi maximum likelihood estimation setting. A size-correction approach is introduced to ensure that the score functions have an asymptotic distribution centered around zero in the local presence of certain nuisance parameters. The outer-product-of-martingale-difference (OPMD) method is used to formulate an estimator for the asymptotic variance of the score functions. The OPMD estimator and the adjusted score functions are used to formulate a computationally simple robust test statistic. The suggested test statistic does not require knowing the presence of spatial dependence in the outcome variable and/or the disturbance terms. The asymptotic distribution of the test statistic is established under the null and local alternative hypotheses. Through Monte Carlo simulations, the finite sample size and power properties of the proposed test statistic are investigated. Finally, two empirical applications are provided to illustrate the practical use of the proposed test statistic.

Testing conditional quantile independence with functional covariate.

We propose a new non-parametric conditional independence test for a scalar response and a functional covariate over a continuum of quantile levels. We build a Cramer-von Mises type test statistic based on an empirical process indexed by random projections of the functional covariate, effectively avoiding the "curse of dimensionality" under the projected hypothesis, which is almost surely equivalent to the null hypothesis. The asymptotic null distribution of the proposed test statistic is obtained under some mild assumptions. The asymptotic global and local power properties of our test statistic are then investigated. We specifically demonstrate that the statistic is able to detect a broad class of local alternatives converging to the null at the parametric rate. Additionally, we recommend a simple multiplier bootstrap approach for estimating the critical values. The finite-sample performance of our statistic is examined through several Monte Carlo simulation experiments. Finally, an analysis of an EEG data set is used to show the utility and versatility of our proposed test statistic.

Two-sample test for stochastic block models via the largest singular value

The stochastic block model is widely used for detecting community structures in network data. However, the research interest in much of the literature focuses on the study of one sample of stochastic block models. Detecting the difference between the two community structures is a less studied issue for stochastic block models. In this article, we propose a novel test statistic based on the largest singular value of a residual matrix obtained by subtracting the geometric mean of two estimated block mean effects from the sum of two observed adjacency matrices. We prove that the null distribution of the proposed test statistic converges in distribution to the Tracy-Widom distribution with index 1, and we show the difference between the two samples for stochastic block models can be tested via the proposed method. We show that the proposed test is asymptotically powerful against alternative models. Further, we extend the proposed method to the degree-corrected stochastic block model. Both simulation studies and real-world data examples indicate that the proposed method works well.

Hypothesis testing of one sample mean vector in distributed frameworks

Distributed frameworks are commonly used in the setting where data are stored in k different local machines and cannot be merged due to privacy protections or the huge sample size. For a random vector X ∈ R p with expectation μ , testing the mean vector H 0 : μ = μ 0 vs H 1 : μ ≠ μ 0 for a given vector μ 0 is a basic problem in statistics. In distributed frameworks, the computation of the centralized test statistics is not privacy-preserving and often requires heavy communication costs, which can be a burden when p or k is large. To deal with this problem, we extend two commonly used centralized test statistics to the distributed ones based on the divide and conquer technique. It is observed that the proposed test statistics are effective and can reduce communication costs and computation complexity. Numerical results confirm the theoretical findings.

A NONPARAMETRIC TEST OF HETEROGENEITY IN CONDITIONAL QUANTILE TREATMENT EFFECTS

This paper proposes a nonparametric test to assess whether there exist heterogeneous quantile treatment effects (QTEs) of an intervention on the outcome of interest across different sub-populations defined by covariates of interest. Specifically, a consistent test statistic based on the Cramér–von Mises type criterion is developed to test if the treatment has a constant quantile effect for all sub-populations defined by covariates of interest. Under some regularity conditions, the asymptotic behaviors of the proposed test statistic are investigated under both the null and alternative hypotheses. Furthermore, a nonparametric Bootstrap procedure is suggested to approximate the finite-sample null distribution of the proposed test; then, the asymptotic validity of the proposed Bootstrap test is theoretically justified. Through Monte Carlo simulations, we demonstrate the power properties of the test in finite samples. Finally, the proposed testing approach is applied to investigate whether there exists heterogeneity for the QTE of maternal smoking during pregnancy on infant birth weight across different age groups of mothers.

Checking normality of model errors under additive distortion measurement errors

We study the goodness-of-fit tests for checking the normality of the model errors under the additive distortion measurement error settings. Neither the response variable nor the covariates can be directly observed but are distorted in additive fashions by an observed confounding variable. The proposed test statistics is based on logarithmic transformed variables with residuals and a particular choice of the kth power covariance-based estimator. The proposed test statistics has three advantages. Firstly, the asymptotic null distribution of the test statistics are obtained with known asymptotic variance. Secondly, the test statistic tests are irrelevant to the model. Thirdly, the proposed test statistics automatically eliminate the additive distortion effects involved in the response and covariates. The simulation studies show the proposed test statistics can be used to check normality when the sample size is very large. A real example is analysed to illustrate its practical usage.

A new goodness-of-fit test for the inverse Gaussian distribution

The Inverse Gaussian (IG) distribution is widely used in practice and therefore an important issue is to develop a powerful goodness-of-fit test (GOF) for this distribution. In this article, we propose and examine a new GOF test for the IG distribution based on a new estimate of Kullback-Leibler (KL) information. The properties of the test statistic are presented. In order to compute the proposed test statistic, parameters of the IG distribution are estimated by maximum likelihood estimators, which are simple explicit estimators. Critical values and the actual sizes of the proposed test are obtained. Through a simulation study, power values of the proposed test are compared with some prominent existing tests. Finally, two illustrative examples are presented and analyzed.

RANK-BASED INDICES FOR TESTING INDEPENDENCE BETWEEN TWO HIGH-DIMENSIONAL VECTORS.

To test independence between two high-dimensional random vectors, we propose three tests based on the rank-based indices derived from Hoeffding's , Blum-Kiefer-Rosenblatt's and Bergsma-Dassios-Yanagimoto's . Under the null hypothesis of independence, we show that the distributions of the proposed test statistics converge to normal ones if the dimensions diverge arbitrarily with the sample size. We further derive an explicit rate of convergence. Thanks to the monotone transformation-invariant property, these distribution-free tests can be readily used to generally distributed random vectors including heavily tailed ones. We further study the local power of the proposed tests and compare their relative efficiencies with two classic distance covariance/correlation based tests in high dimensional settings. We establish explicit relationships between and Pearson's correlation for bivariate normal random variables. The relationships serve as a basis for power comparison. Our theoretical results show that under a Gaussian equicorrelation alternative, (i) the proposed tests are superior to the two classic distance covariance/correlation based tests if the components of random vectors have very different scales; (ii) the asymptotic efficiency of the proposed tests based on and are sorted in a descending order.

A Statistical Testing Strategy Accounting for Random and Nonrandom (Skewed) X-Chromosome Inactivation Identifies Lung Cancer Susceptibility Loci among Smokers.

Lung cancer is the most common cancer worldwide in mortality and the second in incidence. Epidemiological studies found a higher lung cancer risk for smoking women in comparison to men, but these sex differences, irrespective of smoking habits, remain controversial. One of the hypotheses concerns the genetic contribution of the sex chromosomes. However, while genome-wide association studies identified many lung cancer susceptibility loci, these analyses have excluded X-linked loci. To account for nongenetic factors, we first presented an association test based on an additive-multiplicative hazard model accounting for random/nonrandom X-inactivation process. A simulation study was performed to investigate the properties of the proposed test as compared with the Wald test from a Cox model with random X-inactivation process and the partial likelihood ratio test proposed by Xu et al. accounting for nonrandom X-inactivation process. Then, we performed an X chromosome-wide association study on 9,261 individuals from the population-based cohort CARTaGENE to identify susceptibility loci for lung cancer among current and past smokers. We adjusted for the PLCOm2012 lung cancer risk score used in screening programs. Simulation results show the good behavior of the proposed test in terms of power and type I error probability as compared to the Xu et al. and the Wald test. Using the proposed test statistic and adjusting for the PLCOm2012 score, the X chromosome-wide statistical analysis identified two SNPs in low-linkage disequilibrium located in the IL1RAPL1 (IL-1 R accessory protein-like) gene: rs12558491 (p = 2.75×10-9) and rs12835699 (p = 1.26×10-6). For both SNPs, the minor allele was associated with lower lung cancer risk. Adjusting for multiple testing, no signal was detected using the Wald or the Xu et al. likelihood ratio tests. By taking into account smoking behavior and the X-inactivation process, the investigation of the X chromosome has shed a new light on the association between X-linked loci and lung cancer. We identified two loci associated with lung cancer located in the IL1RAPL1 gene. This finding would have been overlooked by examining only results from other test statistics.

Two-sample test of stochastic block models

In this paper, we consider the problem of two-sample test of large networks with community structures. A test statistic is proposed based on the maximum entry of the difference between the two adjacency matrices. Asymptotic null distribution is derived, and the asymptotic power guarantee against the alternative hypothesis is provided. The simulations and real data examples show that the proposed test statistic performs well.

Hypothesis testing on high dimensional quantile regression

Quantile regression has been an important analytical tool in econometrics since it was proposed in 1970s. Many advantages make it still popular in the era of big data. This paper focuses on the testing problems of high-dimensional quantile regression, supplementing to robust methods in the literature of high-dimensional hypothesis testing. We first construct a new test statistic based on the quantile regression score function. The new test statistic avoids the inverse operation of the covariance matrix, and hence becomes applicable to high-dimensional or even ultrahigh-dimensional settings. The proposed method retains robustness for non-Gaussian and heavy-tailed distributions. We then derive the limiting distributions of the proposed test statistic under both the null and the alternative hypotheses. We further investigate the case where the design matrix follows an elliptical distribution. We examined the finite sample performance of our proposed method through Monte Carlo simulations. The numerical comparisons exhibit that our proposed tests outperform some existing methods in terms of controlling Type I error rate and power, when the data deviate from the Gaussian assumptions or are heavy-tailed. We illustrate our proposed high-dimensional quantile testing in financial econometrics, through an empirical analysis of Chinese stock market data.

Performance of Some Modified Test Statistics for Testing the Population Signal to Noise Ratio: Simulation and Applications

This paper considers fifteen existing and proposed test statistics for testing the population SNR. A theoretical comparison among the test statistics is not possible, a Monte Carlo simulation study has been conducted. The performance of the test statistics is based on the empirical size and power of the tests considering a significance level 0.05. The simulation study resulted in some existing and proposed methods performing well in some conditions. For testing SNR=1, 2 and 5, Method 10 performed the best in all simulation conditions. However, for testing SNR=0.5 the proposed Method 12 and for testing SNR=10, the proposed Method 15 performed the best. Two real life data sets are analyzed to illustrate the performance of the test statistics.

Testing conditional independence in casual inference for time series data

In this paper, we propose a new procedure to test conditional independence assumption in studying casual inference for time series data. The conditional independence assumption is transformed to a nonparametric conditional moment test with the help of auxiliary variables which are allowed to affect policy choice but the dependence can be fully captured by potential outcomes and observable controls. When the policy choice is binary, a nonparametric statistic test is developed further for testing the conditional independence assumption conditional on policy propensity score. Under some regular conditions, we show that the proposed test statistics are asymptotically normal under the null hypotheses for time series data. In addition, the performances of the proposed methods are illustrated through Monte Carlo simulations and a real example considered in Angrist and Kuersteiner (2011).

Testing the annual rainfall dispersion in Chaiyaphum, Thailand, by using confidence intervals for the coefficient of variation of an inverse gamma distribution

In Thailand, droughts are regular natural disasters that happen nearly every year due to several factors such as precipitation deficiency, human activity, and the global warming. Since annual rainfall amount fits an inverse gamma (IG) distribution, we wanted to try testing annual rainfall dispersion via the coefficient of variation (CV). Herein, we propose two statistics for testing the CV of an IG distribution based on the Score and Wald methods. We evaluated their performances by means of the Monte Carlo simulations conducted under several shape parameter values for an IG distribution based on empirical type I error rates and powers of the tests. The simulation results reveal that the Wald-method test statistic performed better than the Score-method one in terms of the attained nominal significance level, and is thus recommended for analysis in similar scenarios. Furthermore, the efficacy of the proposed test statistics was illustrated by applying them to the annual rainfall amounts in Chaiyaphum, Thailand.

Statistical models and the Benford hypothesis: a unified framework

The Benford hypothesis is the statement that a random sample is made of realizations of an absolutely continuous random variable distributed according to Benford’s law. Its potential interest spans over many domains such as detection of financial frauds, verification of electoral processes and investigation of scientific measurements. Our aim is to provide a principled framework for the statistical evaluation of this statement. First, we study the probabilistic structure of many classical univariate models when they are framed in the space of the significand and we measure the closeness of each model to the Benford hypothesis. We then obtain two asymptotically equivalent and powerful tests. We show that the proposed test statistics are invariant under scale transformation of the data, a crucial requirement when compliance to the Benford hypothesis is used to corroborate scientific theories. The empirical advantage of the proposed tests is shown through an extensive simulation study. Applications to astrophysical and hydrological data also motivate the methodology.

EM-test for homogeneity in location-scale mixture model with a structural scale

The testing problem for the homogeneity of a location-scale mixture model is fundamental for subsequent statistical inference. In this paper, we employ the EM-test method to test the homogeneity of two commonly encountered location-scale mixture models with a structural scale, and we also establish the theoretical properties of test statistics. Further, to enhance the reliability of the test, based on the computer experiments approach, we develop a Bartlett-corrected approximate distribution for the proposed test statistics. Through Monte Carlo studies and real data example, the effectiveness of the proposed testing procedure is compared with that of the classical one, especially for small or moderate sample sizes.

Sufficient dimension reduction in the presence of controlling variable and missing multivariate response

In this paper, we focus on partial dimension reduction for conditional mean function in the presence of controlling variable when responses are multivariate and missing at random. A weighted-profile least squares estimate based on inverse probability weighted technique is proposed to estimate the central mean subspace. The profile least squares method does not need any distributional assumptions on the covariates, which is different from existing methods in sufficient dimension reduction. It turns out that under some mild conditions, the estimator of central mean subspace is asymptotically normal and root-n consistent. The proposed test statistic as well as its asymptotic distribution for parametric hypothesis tests are obtained. In addition, a BIC-type criterion is used to determine the structural dimension of the central mean subspace. Its consistency is also established. Both simulated and real data analysis results demonstrate promising performance of the proposed sufficient dimension reduction estimation method.

Parametric hypothesis tests for exponentiality under multiplicative distortion measurement errors data

In this paper, we proposed a parametric hypothesis test of the multiplicative distortion model under the exponentially distributed but unobserved random variable. The unobservable variable is distorted in a multiplicative fashion by an observed confounding variable. Firstly, some new test statistics are proposed to checking the exponential distribution assumption without distortion effects. Next, we proposed several test statistics when the variable is distorted in the multiplicative fashion. For the latter, the proposed test statistics automatically eliminate the distortion effects involved in the unobserved variable. The proposed test statistics with or without distortions are all asymptotical free, and the asymptotic null distribution of the test statistics are obtained with known asymptotic variances. We conduct Monte Carlo simulation experiments to examine the performance of the proposed test statistics. These methods are applied to analyze four real datasets for illustrations.