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Nonparametric two sample testing is a decision theoretic problem that involves identifying differences between two random variables without making parametric assumptions about their underlying distributions. We refer to the most common…
Two-sample testing is a fundamental problem in statistics, and many famous two-sample tests are designed to be fully non-parametric. These existing methods perform well with location and scale shifts but are less robust when faced with more…
As a common step in refining their scientific inquiry, investigators are often interested in performing some screening of a collection of given statistical hypotheses. For example, they may wish to determine whether any one of several…
A new family of nonparametric statistics, the r-statistics, is introduced. It consists of counting the number of records of the cumulative sum of the sample. The single-sample r-statistic is almost as powerful as Student's t-statistic for…
In the problem of composite hypothesis testing, identifying the potential uniformly most powerful (UMP) unbiased test is of great interest. Beyond typical hypothesis settings with exponential family, it is usually challenging to prove the…
A new method based on the rejection sampling for finding statistical tests is proposed. This method is conceptually intuitive, easy to implement, and applicable for arbitrary dimension. To illustrate its potential applicability, three…
Network (graph) data analysis is a popular research topic in statistics and machine learning. In application, one is frequently confronted with graph two-sample hypothesis testing where the goal is to test the difference between two graph…
Comparing two population means of network data is of paramount importance in a wide range of scientific applications. Many existing network inference solutions focus on global testing of entire networks, without comparing individual network…
Simulation offers a simple and flexible way to estimate the power of a clinical trial when analytic formulae are not available. The computational burden of using simulation has, however, restricted its application to only the simplest of…
Hybrid studies allow investigators to simultaneously study an intervention effectiveness outcome and an implementation research outcome. In particular, type 2 hybrid studies support research that places equal importance on both outcomes…
Modern studies increasingly leverage outcomes predicted by machine learning and artificial intelligence (AI/ML) models, and recent work, such as prediction-powered inference (PPI), has developed valid downstream statistical inference…
In this paper, we propose novel, fully Bayesian non-parametric tests for one-sample and two-sample multivariate location problems. We model the underlying distribution using a Dirichlet process prior, and develop a testing procedure based…
Multivariate goodness-of-fit and two-sample tests are important components of many nuclear and particle physics analyses. While a variety of powerful methods are available if the dimensionality of the feature space is small, such tests…
This paper contains two finite-sample results concerning the sign test. First, we show that the sign-test is unbiased with independent, non-identically distributed data for both one-sided and two-sided hypotheses. The proof for the…
Empirical cumulative distribution functions (ECDFs) have been used to test the hypothesis that two samples come from the same distribution since the seminal contribution by Kolmogorov and Smirnov. This paper describes a statistic which is…
Two-sample and independence tests with the kernel-based MMD and HSIC have shown remarkable results on i.i.d. data and stationary random processes. However, these statistics are not directly applicable to non-stationary random processes, a…
We investigate one/two-sample mean tests for high-dimensional compositional data when the number of variables is comparable with the sample size, as commonly encountered in microbiome research. Existing methods mainly focus on max-type test…
This article gives a synopsis on new developments in affine invariant tests for multivariate normality in an i.i.d.-setting, with special emphasis on asymptotic properties of several classes of weighted $L^2$-statistics. Since weighted…
This paper proposes a new class of nonparametric tests for the correct specification of models based on conditional moment restrictions, paying particular attention to generalized propensity score models. The test procedure is based on two…
Along the lines of Janssen's and Pfanzagl's work the testing theory for statistical functionals is further developed for non-parametric one-sample problems. Efficient tests for the one-sided and two-sided problems are derived for…