Related papers: A Test for Separability in Covariance Operators of…

Identifying dependency in multivariate data is a common inference task that arises in numerous applications. However, existing nonparametric independence tests typically require computation that scales at least quadratically with the sample…

For spatially dependent functional data, a generalized Karhunen-Lo\`{e}ve expansion is commonly used to decompose data into an additive form of temporal components and spatially correlated coefficients. This structure provides a convenient…

We propose new statistical tests, in high-dimensional settings, for testing the independence of two random vectors and their conditional independence given a third random vector. The key idea is simple, i.e., we first transform each…

In this paper, we propose a new test for checking the parametric form of the conditional variance based on distance covariance in nonlinear and nonparametric regression models. Inherit from the nice properties of distance covariance, our…

The issue addressed in this paper is that of testing for common breaks across or within equations of a multivariate system. Our framework is very general and allows integrated regressors and trends as well as stationary regressors. The null…

Accurately estimating the proportion of true signals among a large number of variables is crucial for enhancing the precision and reliability of scientific research. Traditional signal proportion estimators often assume independence among…

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…

In this paper we study covariance estimation with missing data. We consider missing data mechanisms that can be independent of the data, or have a time varying dependency. Additionally, observed variables may have arbitrary (non uniform)…

Identifying an appropriate covariance function is one of the primary interests in spatial and spatio-temporal statistics because it allows researchers to analyze the dependence structure of the random process. For this purpose, spatial…

Motivated by the need to statistically quantify the difference between two spatio-temporal datasets that arise in climate downscaling studies, we propose new tests to detect the differences of the covariance operators and their associated…

The state-of-the-art methods for estimating high-dimensional covariance matrices all shrink the eigenvalues of the sample covariance matrix towards a data-insensitive shrinkage target. The underlying shrinkage transformation is either…

The hypothesis of randomness is fundamental in statistical machine learning and in many areas of nonparametric statistics; it says that the observations are assumed to be independent and coming from the same unknown probability…

Many inference techniques for multivariate data analysis assume that the rows of the data matrix are realizations of independent and identically distributed random vectors. Such an assumption will be met, for example, if the rows of the…

Given a small random sample of $n$-bit strings labeled by an unknown Boolean function, which properties of this function can be tested computationally efficiently? We show an equivalence between properties that are efficiently testable from…

Testing independence among a number of (ultra) high-dimensional random samples is a fundamental and challenging problem. By arranging $n$ identically distributed $p$-dimensional random vectors into a $p \times n$ data matrix, we investigate…

The paper introduces robust independence tests with non-asymptotically guaranteed significance levels for stochastic linear time-invariant systems, assuming that the observed outputs are synchronous, which means that the systems are driven…

We propose a robust test for the equality of the covariance structures in two functional samples. The test statistic has a chi-square asymptotic distribution with a known number of degrees of freedom, which depends on the level of dimension…

The distance covariance of two random vectors is a measure of their dependence. The empirical distance covariance and correlation can be used as statistical tools for testing whether two random vectors are independent. We propose an analogs…

This paper studies sparse covariance operator estimation for nonstationary processes with sharply varying marginal variance and small correlation lengthscale. We introduce a covariance operator estimator that adaptively thresholds the…

Test of independence is of fundamental importance in modern data analysis, with broad applications in variable selection, graphical models, and causal inference. When the data is high dimensional and the potential dependence signal is…