Related papers: A Note on High Dimensional Two Sample Mean Test
This paper presents a selective survey of recent developments in statistical inference and multiple testing for high-dimensional regression models, including linear and logistic regression. We examine the construction of confidence…
The t-statistic is a widely-used scale-invariant statistic for testing the null hypothesis that the mean is zero. Martingale methods enable sequential testing with the t-statistic at every sample size, while controlling the probability of…
When data analysts train a classifier and check if its accuracy is significantly different from chance, they are implicitly performing a two-sample test. We investigate the statistical properties of this flexible approach in the…
We are interested in testing general linear hypotheses in a high-dimensional multivariate linear regression model. The framework includes many well-studied problems such as two-sample tests for equality of population means, MANOVA and…
Robust classification algorithms have been developed in recent years with great success. We take advantage of this development and recast the classical two-sample test problem in the framework of classification. Based on the estimates of…
This paper introduces a novel two-sample test for a broad class of orthogonally equivalent positive definite symmetric matrix distributions. Our test is the first of its kind and we derive its asymptotic distribution. To estimate the test…
This article deals with the problem of testing conditional independence between two random vectors ${\bf X}$ and ${\bf Y}$ given a confounding random vector ${\bf Z}$. Several authors have considered this problem for multivariate data.…
We propose a new class of goodness-of-fit tests for the inverse Gaussian distribution. The proposed tests are weighted $L^2$-type tests depending on a tuning parameter. We develop the asymptotic theory under the null hypothesis and under a…
In order to adapt the Wasserstein distance to the large sample multivariate non-parametric two-sample problem, making its application computationally feasible, permutation tests based on the Sinkhorn divergence between probability vectors…
This paper provides some useful tests for fitting a parametric single-index regression model when covariates are measured with error and validation data is available. We propose two tests whose consistency rates do not depend on the…
This paper deals with two-sample tests for functional time series data, which have become widely available in conjunction with the advent of modern complex observation systems. Here, particular interest is in evaluating whether two sets of…
Testing independence is of significant interest in many important areas of large-scale inference. Using extreme-value form statistics to test against sparse alternatives and using quadratic form statistics to test against dense alternatives…
This paper develops a novel change point identification method for high-dimensional data using random projections. By projecting high-dimensional time series into a one-dimensional space, we are able to leverage the rich literature for…
Information in the time distribution of points in a state space reconstructed from observed data yields a test for ``nonstationarity''. Framed in terms of a statistical hypothesis test, this numerical algorithm can discern whether some…
Given observations from a stationary time series, permutation tests allow one to construct exactly level $\alpha$ tests under the null hypothesis of an i.i.d. (or, more generally, exchangeable) distribution. On the other hand, when the null…
We consider the structural change in a class of discrete valued time series that the conditional distribution follows a one-parameter exponential family. We propose a change-point test based on the maximum likelihood estimator of the…
We propose two model-free, permutation-based tests of independence between a pair of random variables. The tests can be applied to samples from any bivariate distribution: continuous, discrete or mixture of those, with light tails or heavy…
Reliable inference for spatial regression remains challenging because it requires the correct specification of the spatial dependence structure, the mean trend, and the error distribution. Existing parametric testing methods rely on…
The problem of testing for the parametric form of the conditional variance is considered in a fully nonparametric regression model. A test statistic based on a weighted $L_2$-distance between the empirical characteristic functions of…
We present the results of a large number of simulation studies regarding the power of various goodness-of-fit as well as non-parametric two-sample tests for multivariate data. In two dimensions this includes both continuous and discrete…