Related papers: Deviation Tests for a High-dimensional Mean
We consider the problem of sequentially testing for changes in the mean parameter of a time series, compared to a benchmark period. Most tests in the literature focus on the null hypothesis of a constant mean versus the alternative of a…
Two-sample testing is a fundamental problem in statistics. Despite its long history, there has been renewed interest in this problem with the advent of high-dimensional and complex data. Specifically, in the machine learning literature,…
In the context of functional data analysis, we propose new two sample tests for homogeneity. Based on some well-known depth measures, we construct four different statistics in order to measure distance between the two samples. A simulation…
We consider the problem of distributed mean estimation (DME), in which $n$ machines are each given a local $d$-dimensional vector $x_v \in \mathbb{R}^d$, and must cooperate to estimate the mean of their inputs $\mu = \frac 1n\sum_{v = 1}^n…
In this article, we introduce a novel discrepancy called the maximum variance discrepancy for the purpose of measuring the difference between two distributions in Hilbert spaces that cannot be found via the maximum mean discrepancy. We also…
Asymptotic methods for hypothesis testing in high-dimensional data usually require the dimension of the observations to increase to infinity, often with an additional relationship between the dimension (say, $p$) and the sample size (say,…
The standardized mean difference (SMD) is a widely used measure of effect size, particularly common in psychology, clinical trials, and meta-analysis involving continuous outcomes. Traditionally, under the equal variance assumption, the SMD…
We consider a high-dimensional mean estimation problem over a binary hidden Markov model, which illuminates the interplay between memory in data, sample size, dimension, and signal strength in statistical inference. In this model, an…
The Wilcoxon signed-rank test and the Wilcoxon-Mann-Whitney test are commonly employed in one sample and two sample mean tests for one-dimensional hypothesis problems. For high-dimensional mean test problems, we calculate the asymptotic…
Hypothesis testing is a statistical inference approach used to determine whether data supports a specific hypothesis. An important type is the two-sample test, which evaluates whether two sets of data points are from identical…
Large-scale multiple testing under static factor models is widely used to detect sparse signals in high-dimensional data. However, static factor models are arguably too stringent because they ignore serial correlation, which seriously…
Testing mutual independence among multiple random variables is a fundamental problem in statistics, with wide applications in genomics, finance, and neuroscience. In this paper, we propose a new class of tests for high-dimensional mutual…
High dimensional hypothesis test deals with models in which the number of parameters is significantly larger than the sample size. Existing literature develops a variety of individual tests. Some of them are sensitive to the dense and small…
We revisit the problem of Gaussian mean testing in a distributed, communication constrained setting, where each of $n$ users independently observes samples from an unknown $d$-dimensional spherical Gaussian distribution…
Testing for the equality of two high-dimensional distributions is a challenging problem, and this becomes even more challenging when the sample size is small. Over the last few decades, several graph-based two-sample tests have been…
We use a system of first-order partial differential equations that characterize the moment generating function of the $d$-variate standard normal distribution to construct a class of affine invariant tests for normality in any dimension. We…
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…
The recent measurement of an anomalous like-sign dimuon asymmetry by the D0 collaboration has prompted theoretical speculation on possible sources of physics beyond the Standard Model that may affect lifetimes and lifetime differences in…
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…
In this article, we present a nonparametric method for the general two-sample problem involving functional random variables modelled as elements of a separable Hilbert space ${\cal H}$. First, we present a general recipe based on linear…