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We study two nonparametric tests of the hypothesis that a sequence of independent observations is identically distributed against the alternative that at a single change point the distribution changes. The tests are based on the Cramer-von…
Tests based on sample mean vectors and sample spatial signs have been studied in the recent literature for high dimensional data with the dimension larger than the sample size. For suitable sequences of alternatives, we show that the powers…
We study two-sample variable selection: identifying variables that discriminate between the distributions of two sets of data vectors. Such variables help scientists understand the mechanisms behind dataset discrepancies. Although…
Moment restrictions and their conditional counterparts emerge in many areas of machine learning and statistics ranging from causal inference to reinforcement learning. Estimators for these tasks, generally called methods of moments, include…
This paper defines an alternative notion, described as data-based, of geometric quantiles on Hadamard spaces, in contrast to the existing methodology, described as parameter-based. In addition to having the same desirable properties as…
Distributional reinforcement learning (DRL) has achieved empirical success in various domains. One core task in DRL is distributional policy evaluation, which involves estimating the return distribution $\eta^\pi$ for a given policy $\pi$.…
We propose a new one-sample test for normality in a Reproducing Kernel Hilbert Space (RKHS). Namely, we test the null-hypothesis of belonging to a given family of Gaussian distributions. Hence our procedure may be applied either to test…
Consider two random variables contaminated by two unknown transformations. The aim of this paper is to test the equality of those transformations. Two cases are distinguished: first, the two random variables have known distributions.…
Many large-scale testing procedures learn signal structure from the data to boost power. Direct data reuse can inflate Type-I error ("double dipping"), so a common remedy is masking: withholding some information during learning and using it…
When observations are independent, formulae and software are readily available to plan and design studies of appropriate size and power to detect important associations. When observations are correlated or clustered, results obtained from…
Recently, the importance of analysing data and collecting valuable insight efficiently has been increasing in various fields. Estimating mutual information (MI) plays a critical role to investigate the relationship among multiple random…
We provide a distribution-free test that can be used to determine whether any two joint distributions $p$ and $q$ are statistically different by inspection of a large enough set of samples. Following recent efforts from Long et al. [1], we…
We propose a two-sample test for the means of high-dimensional data when the data dimension is much larger than the sample size. Hotelling's classical $T^2$ test does not work for this "large $p$, small $n$" situation. The proposed test…
In this paper, we introduce a ${\mathcal L}_2$ type test for testing mutual independence and banded dependence structure for high dimensional data. The test is constructed based on the pairwise distance covariance and it accounts for the…
High-dimensional k-sample comparison is a common applied problem. We construct a class of easy-to-implement nonparametric distribution-free tests based on new tools and unexplored connections with spectral graph theory. The test is shown to…
We propose a framework to construct practical kernel-based two-sample tests from the family of $f$-divergences. The test statistic is computed from the witness function of a regularized variational representation of the divergence, which we…
We revisit the classical causal inference problem of estimating the average treatment effect in the presence of fully observed confounding variables using two-stage semiparametric methods. In existing theoretical studies of methods such as…
A basic issue in both teaching of and practice of statistics is the interplay between modelling assumptions and inference performance. The general message conveyed is that stronger assumptions lead to better statistical performance of the…
We propose a class of two-sample statistics for testing the equality of proportions and the equality of survival functions. We build our proposal on a weighted combination of a score test for the difference in proportions and a Weighted…
Longitudinal studies frequently incorporate covariates that evolve over time, creating complex dependence structures between outcomes and predictors. When covariates are time dependent, standard power analysis tools--largely developed for…