Related papers: Two-Sample Testing in High-Dimensional Models
This work is motivated by learning the individualized minimal clinically important difference, a vital concept to assess clinical importance in various biomedical studies. We formulate the scientific question into a high-dimensional…
In analyzing high-dimensional models, sparsity of the model parameter is a common but often undesirable assumption. In this paper, we study the following two-sample testing problem: given two samples generated by two high-dimensional linear…
Two-sample tests evaluate whether two samples are realizations of the same distribution (the null hypothesis) or two different distributions (the alternative hypothesis). We consider a new setting for this problem where sample features are…
Two-sided statistical tests and p-values are well defined only when the test statistic in question has a symmetric distribution. A new two-sided p-value called conditional p-value $P_C$ is introduced here. It is closely related to the…
Testing the equality in distributions of multiple samples is a common task in many fields. However, this problem for high-dimensional or non-Euclidean data has not been well explored. In this paper, we propose new nonparametric tests based…
We propose a test of many zero parameter restrictions in a high dimensional linear iid regression model with $k$ $>>$ $n$ regressors. The test statistic is formed by estimating key parameters one at a time based on many low dimension…
Fitting high-dimensional statistical models often requires the use of non-linear parameter estimation procedures. As a consequence, it is generally impossible to obtain an exact characterization of the probability distribution of the…
After variable selection, standard inferential procedures for regression parameters may not be uniformly valid; there is no finite-sample size at which a standard test is guaranteed to approximately attain its nominal size. This problem is…
Non-probability samples become increasingly popular in survey statistics but may suffer from selection biases that limit the generalizability of results to the target population. We consider integrating a non-probability sample with a…
A two-sample hypothesis test is a statistical procedure used to determine whether the distributions generating two samples are identical. We consider the two-sample testing problem in a new scenario where the sample measurements (or sample…
Focusing on polygenic signal detection in high dimensional genetic association studies of complex traits, we develop an adaptive test for generalized linear models to accommodate different alternatives. To facilitate valid post-selection…
Suppose that we are interested in the comparison of two independent categorical variables. Suppose also that the population is divided into subpopulations or groups. Notice that the distribution of the target variable may vary across…
In this paper, we introduce an innovative testing procedure for assessing individual hypotheses in high-dimensional linear regression models with measurement errors. This method remains robust even when either the X-model or Y-model is…
The two-sample hypothesis testing problem is studied for the challenging scenario of high dimensional data sets with small sample sizes. We show that the two-sample hypothesis testing problem can be posed as a one-class set classification…
One of the fundamental problems in machine learning is the estimation of a probability distribution from data. Many techniques have been proposed to study the structure of data, most often building around the assumption that observations…
Kernel two-sample tests have been widely used, and the development of efficient methods for high-dimensional, large-scale data is receiving increasing attention in the big data era. However, existing methods, such as the maximum mean…
For random samples of size n obtained from p-variate normal distributions, we consider the classical likelihood ratio tests (LRT) for their means and covariance matrices in the high-dimensional setting. These test statistics have been…
Two-sample hypothesis testing-determining whether two sets of data are drawn from the same distribution-is a fundamental problem in statistics and machine learning with broad scientific applications. In the context of nonparametric testing,…
We develop a theoretical framework for sample splitting in A/B testing environments, where data for each test are partitioned into two splits to measure methodological performance when the true impacts of tests are unobserved. We show that…
This paper introduces several depths for random sets with possibly non-convex realisations, proposes ways to estimate the depths based on the samples and compares them with existing ones. The depths are further applied for the comparison…