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Recognizing, quantifying and visualizing associations between two variables is increasingly important. This paper investigates how a new function-valued measure of dependence, the quantile dependence function, can be used to construct tests…
We study an independence test based on distance correlation for random fields $(X,Y)$. We consider the situations when $(X,Y)$ is observed on a lattice with equidistant grid sizes and when $(X,Y)$ is observed at random locations. We provide…
Recently, the binary expansion testing framework was introduced to test the independence of two continuous random variables by utilizing symmetry statistics that are complete sufficient statistics for dependence. We develop a new test based…
In this work we address the problem of detecting whether a sampled probability distribution of a random variable $V$ has infinite first moment. This issue is notably important when the sample results from complex numerical simulation…
In general, randomness tests included in a test suite are not independent of each other. This renders it difficult to fix a rational criterion through the whole test suite with an explicit significance level. In this paper, we focus on the…
The achievable error-exponent pairs for the type I and type II errors are characterized in a hypothesis testing setup where the observation consists of independent and identically distributed samples from either a known joint probability…
Experiments often yield non-identically distributed data for statistical analysis. Tests of hypothesis under such set-ups are generally performed using the likelihood ratio test, which is non-robust with respect to outliers and model…
This paper studies distributed binary test of statistical independence under communication (information bits) constraints. While testing independence is very relevant in various applications, distributed independence test is particularly…
The statistics and machine learning communities have recently seen a growing interest in classification-based approaches to two-sample testing. The outcome of a classification-based two-sample test remains a rejection decision, which is not…
Ultrahigh-dimensional variable selection plays an increasingly important role in contemporary scientific discoveries and statistical research. Among others, Fan and Lv [J. R. Stat. Soc. Ser. B Stat. Methodol. 70 (2008) 849-911] propose an…
This paper proposes a nonparametric test of pairwise independence of one random variable from a large pool of other random variables. The test statistic is the maximum of several Chatterjee's rank correlations and critical values are…
Most of the popular dependence measures for two random variables $X$ and $Y$ (such as Pearson's and Spearman's correlation, Kendall's $\tau$ and Gini's $\gamma$) vanish whenever $X$ and $Y$ are independent. However, neither does a vanishing…
We study the problem of lossless feature selection for a $d$-dimensional feature vector $X=(X^{(1)},\dots ,X^{(d)})$ and label $Y$ for binary classification as well as nonparametric regression. For an index set $S\subset \{1,\dots ,d\}$,…
A common problem in genetics is that of testing whether a set of highly dependent gene expressions differ between two populations, typically in a high-dimensional setting where the data dimension is larger than the sample size. Most…
We propose an independence test for random variables valued into metric spaces by using a test statistic obtained from appropriately centering and rescaling the squared Hilbert-Schmidt norm of the usual empirical estimator of normalized…
We analyze the extreme value dependence of independent, not necessarily identically distributed multivariate regularly varying random vectors. More specifically, we propose estimators of the spectral measure locally at some time point and…
We study the problem of independence testing given independent and identically distributed pairs taking values in a $\sigma$-finite, separable measure space. Defining a natural measure of dependence $D(f)$ as the squared $L^2$-distance…
The need to test whether two random vectors are independent has spawned a large number of competing measures of dependence. We are interested in nonparametric measures that are invariant under strictly increasing transformations, such as…
Independence testing plays a central role in statistical and causal inference from observational data. Standard independence tests assume that the data samples are independent and identically distributed (i.i.d.) but that assumption is…
The conditional independence assumption has recently appeared in a growing body of literature on the estimation of multivariate mixtures. We consider here conditionally independent multivariate mixtures of power series distributions with…