Related papers: Directional testing for high-dimensional multivari…
This paper proposes various nonparametric tools based on measure transportation for directional data. We use optimal transports to define new notions of distribution and quantile functions on the hypersphere, with meaningful quantile…
Real-life data are often non-IID due to complex distributions and interactions, and the sensitivity to the distribution of samples can differ among learning models. Accordingly, a key question for any supervised or unsupervised model is…
In this paper, we have developed new multistage tests which guarantee prescribed level of power and are more efficient than previous tests in terms of average sampling number and the number of sampling operations. Without truncation, the…
High-dimensional data, where the dimension of the feature space is much larger than sample size, arise in a number of statistical applications. In this context, we construct the generalized multivariate sign transformation, defined as a…
The asymptotically optimal hypothesis testing problem with the general sources as the null and alternative hypotheses is studied under exponential-type error constraints on the first kind of error probability. Our fundamental philosophy in…
Many testing problems are readily amenable to randomised tests such as those employing data splitting. However despite their usefulness in principle, randomised tests have obvious drawbacks. Firstly, two analyses of the same dataset may…
In this paper we consider testing the equality of probability vectors of two independent multinomial distributions in high dimension. The classical chi-square test may have some drawbacks in this case since many of cell counts may be zero…
The classic problems of testing uniformity of and learning a discrete distribution, given access to independent samples from it, are examined under general $\ell_p$ metrics. The intuitions and results often contrast with the classic…
Characteristic-function based goodness-of-fit tests are suggested for multivariate observations. The test statistics, which are straightforward to compute, are defined as two-sample criteria measuring discrepancy between multivariate ranks…
We develop the distribution of the number of hypotheses found to be statistically significant using the rule from Benjamini and Hochberg (1995) for controlling the false discovery rate (FDR). This distribution has both a small sample form…
In this paper, we study inference for high-dimensional data characterized by small sample sizes relative to the dimension of the data. In particular, we provide an infinite-dimensional framework to study statistical models that involve…
Global hypothesis tests are a useful tool in the context of, e.g, clinical trials, genetic studies or meta analyses, when researchers are not interested in testing individual hypotheses, but in testing whether none of the hypotheses is…
In this paper new tests for the independence of two high-dimensional vectors are investigated. We consider the case where the dimension of the vectors increases with the sample size and propose multivariate analysis of variance-type…
Symmetry plays a central role in the sciences, machine learning, and statistics. For situations in which data are known to obey a symmetry, a multitude of methods that exploit symmetry have been developed. Statistical tests for the presence…
We consider the problem of testing the equality of conditional distributions of a response variable given a vector of covariates between two populations. Such a hypothesis testing problem can be motivated from various machine learning and…
We consider linear regression in the high-dimensional regime where the number of observations $n$ is smaller than the number of parameters $p$. A very successful approach in this setting uses $\ell_1$-penalized least squares (a.k.a. the…
A Poisson Binomial distribution over $n$ variables is the distribution of the sum of $n$ independent Bernoullis. We provide a sample near-optimal algorithm for testing whether a distribution $P$ supported on $\{0,...,n\}$ to which we have…
This article inspects whether a multivariate distribution is different from a specified distribution or not, and it also tests the equality of two multivariate distributions. In the course of this study, a graphical tool-kit using…
We study the problem of testing discrete distributions with a focus on the high probability regime. Specifically, given samples from one or more discrete distributions, a property $\mathcal{P}$, and parameters $0< \epsilon, \delta <1$, we…
We develop tests for high-dimensional covariance matrices under a generalized elliptical model. Our tests are based on a central limit theorem (CLT) for linear spectral statistics of the sample covariance matrix based on self-normalized…