arXiv subjects

Zheyang Wu

Publications and source records attributed to Zheyang Wu.

8 recordsLinked to original sources

arXiv2025

Optimal Adjustment and Combination of Independent Discrete $p$-Values

Combining p-values from multiple independent tests is a fundamental task in statistical inference, but presents unique challenges when the p-values are discrete. We extend a recent optimal transport-based framework for combining discrete p-values, which constructs a continuous surrogate distribution by minimizing the Wasserstein distance between the transformed discrete null and its continuous analogue. We provide a unified approach for several classical combination methods, including Fisher's, Pearson's, George's, Stouffer's, and Edgington's statistics. Our theoretical analysis and extensive simulations show that accurate Type I error control is achieved when the variance of the adjusted discrete statistic closely matches that of the continuous case. We further demonstrate that, when the likelihood ratio test is a monotonic function of a combination statistic, the proposed approximation achieves power comparable to the uniformly most powerful (UMP) test. The methodology is illustrated with a genetic association study of rare variants using case-control data, and is implemented in the R package DPComb.

stat.ME↗

arXiv2023

A minimum Wasserstein distance approach to Fisher's combination of independent discrete p-values

This paper introduces a comprehensive framework to adjust a discrete test statistic for improving its hypothesis testing procedure. The adjustment minimizes the Wasserstein distance to a null-approximating continuous distribution, tackling some fundamental challenges inherent in combining statistical significances derived from discrete distributions. The related theory justifies Lancaster's mid-p and mean-value chi-squared statistics for Fisher's combination as special cases. However, in order to counter the conservative nature of Lancaster's testing procedures, we propose an updated null-approximating distribution. It is achieved by further minimizing the Wasserstein distance to the adjusted statistics within a proper distribution family. Specifically, in the context of Fisher's combination, we propose an optimal gamma distribution as a substitute for the traditionally used chi-squared distribution. This new approach yields an asymptotically consistent test that significantly improves type I error control and enhances statistical power.

math.ST↗

arXiv2020

An efficient and accurate approximation to the distribution of quadratic forms of Gaussian variables

In computational and applied statistics, it is of great interest to get fast and accurate calculation for the distributions of the quadratic forms of Gaussian random variables. This paper presents a novel approximation strategy that contains two developments. First, we propose a faster numerical procedure in computing the moments of the quadratic forms. Second, we establish a general moment-matching framework for distribution approximation, which covers existing approximation methods for the distributions of the quadratic forms of Gaussian variables. Under this framework, a novel moment-ratio method (MR) is proposed to match the ratio of skewness and kurtosis based on the gamma distribution. Our extensive simulations show that 1) MR is almost as accurate as the exact distribution calculation and is much more efficient; 2) comparing with existing approximation methods, MR significantly improves the accuracy of approximating far right tail probabilities. The proposed method has wide applications. For example, it is a better choice than existing methods for facilitating hypothesis testing in big data analysis, where efficient and accurate calculation of very small $p$-values is desired. An R package Qapprox that implements related methods is available on CRAN.

stat.ME↗

arXiv2020

Accurate $p$-Value Calculation for Generalized Fisher's Combination Tests Under Dependence

Combining dependent tests of significance has broad applications but the $p$-value calculation is challenging. Current moment-matching methods (e.g., Brown's approximation) for Fisher's combination test tend to significantly inflate the type I error rate at the level less than 0.05. It could lead to significant false discoveries in big data analyses. This paper provides several more accurate and computationally efficient $p$-value calculation methods for a general family of Fisher type statistics, referred as the GFisher. The GFisher covers Fisher's combination, Good's statistic, Lancaster's statistic, weighted Z-score combination, etc. It allows a flexible weighting scheme, as well as an omnibus procedure that automatically adapts proper weights and degrees of freedom to a given data. The new $p$-value calculation methods are based on novel ideas of moment-ratio matching and joint-distribution surrogating. Systematic simulations show that they are accurate under multivariate Gaussian, and robust under the generalized linear model and the multivariate $t$-distribution, down to at least $10^{-6}$ level. We illustrate the usefulness of the GFisher and the new $p$-value calculation methods in analyzing both simulated and real data of gene-based SNP-set association studies in genetics. Relevant computation has been implemented into R package $GFisher$.

stat.ME↗

arXiv2018

Generalized Goodness-Of-Fit Tests for Correlated Data

This paper concerns the problem of applying the generalized goodness-of-fit (gGOF) type tests for analyzing correlated data. The gGOF family broadly covers the maximum-based testing procedures by ordered input $p$-values, such as the false discovery rate procedure, the Kolmogorov-Smirnov type statistics, the $ϕ$-divergence family, etc. Data analysis framework and a novel $p$-value calculation approach is developed under the Gaussian mean model and the generalized linear model (GLM). We reveal the influence of data transformations to the signal-to-noise ratio and the statistical power under both sparse and dense signal patterns and various correlation structures. In particular, the innovated transformation (IT), which is shown equivalent to the marginal model-fitting under the GLM, is often preferred for detecting sparse signals in correlated data. We propose a testing strategy called the digGOF, which combines a double-adaptation procedure (i.e., adapting to both the statistic's formula and the truncation scheme of the input $p$-values) and the IT within the gGOF family. It features efficient computation and robust adaptation to the family-retained advantages for given data. Relevant approaches are assessed by extensive simulations and by genetic studies of Crohn's disease and amyotrophic lateral sclerosis. Computations have been included into the R package SetTest available on CRAN.

stat.ME↗

arXiv2018

TFisher Tests: Optimal and Adaptive Thresholding for Combining $p$-Values

For testing a group of hypotheses, tremendous $p$-value combination methods have been developed and widely applied since 1930's. Some methods (e.g., the minimal $p$-value) are optimal for sparse signals, and some others (e.g., Fisher's combination) are optimal for dense signals. To address a wide spectrum of signal patterns, this paper proposes a unifying family of statistics, called TFisher, with general $p$-value truncation and weighting schemes. Analytical calculations for the $p$-value and the statistical power of TFisher under general hypotheses are given. Optimal truncation and weighting parameters are studied based on Bahadur Efficiency (BE) and the proposed Asymptotic Power Efficiency (APE), which is superior to BE for studying the signal detection problem. A soft-thresholding scheme is shown to be optimal for signal detection in a large space of signal patterns. When prior information of signal pattern is unavailable, an omnibus test, oTFisher, can adapt to the given data. Simulations evidenced the accuracy of calculations and validated the theoretical properties. The TFisher tests were applied to analyzing a whole exome sequencing data of amyotrophic lateral sclerosis. Relevant tests and calculations have been implemented into an R package $TFisher$ and published on the CRAN.

stat.ME↗

arXiv2017

Distributions and Statistical Power of Optimal Signal-Detection Methods In Finite Cases

In big data analysis for detecting rare and weak signals among $n$ features, some grouping-test methods such as Higher Criticism test (HC), Berk-Jones test (B-J), and $ϕ$-divergence test share the similar asymptotical optimality when $n \rightarrow \infty$. However, in practical data analysis $n$ is frequently small and moderately large at most. In order to properly apply these optimal tests and wisely choose them for practical studies, it is important to know how to get the p-values and statistical power of them. To address this problem in an even broader context, this paper provides analytical solutions for a general family of goodness-of-fit (GOF) tests, which covers these optimal tests. For any given i.i.d. and continuous distributions of the input test statistics of the $n$ features, both p-value and statistical power of such a GOF test can be calculated. By calculation we compared the finite-sample performances of asymptotically optimal tests under the normal mixture alternative. Results show that HC is the best choice when signals are rare, while B-J is more robust over various signal patterns. In the application to a real genome-wide association study, results illustrate that the p-value calculation works well, and the optimal tests have potentials for detecting novel disease genes with weak genetic effects. The calculations have been implemented in an R package SetTest and published on the CRAN.

math.ST↗

arXiv2014

Detection boundary and Higher Criticism approach for rare and weak genetic effects

Genome-wide association studies (GWAS) have identified many genetic factors underlying complex human traits. However, these factors have explained only a small fraction of these traits' genetic heritability. It is argued that many more genetic factors remain undiscovered. These genetic factors likely are weakly associated at the population level and sparsely distributed across the genome. In this paper, we adapt the recent innovations on Tukey's Higher Criticism (Tukey [The Higher Criticism (1976) Princeton Univ.]; Donoho and Jin [Ann. Statist. 32 (2004) 962-994]) to SNP-set analysis of GWAS, and develop a new theoretical framework in large-scale inference to assess the joint significance of such rare and weak effects for a quantitative trait. In the core of our theory is the so-called detection boundary, a curve in the two-dimensional phase space that quantifies the rarity and strength of genetic effects. Above the detection boundary, the overall effects of genetic factors are strong enough for reliable detection. Below the detection boundary, the genetic factors are simply too rare and too weak for reliable detection. We show that the HC-type methods are optimal in that they reliably yield detection once the parameters of the genetic effects fall above the detection boundary and that many commonly used SNP-set methods are suboptimal. The superior performance of the HC-type approach is demonstrated through simulations and the analysis of a GWAS data set of Crohn's disease.

stat.AP↗