Related papers: Test of Covariance and Correlation Matrices
Consider a set of multivariate distributions, $F_1,\dots,F_M$, aiming to explain the same phenomenon. For instance, each $F_m$ may correspond to a different candidate background model for calibration data, or to one of many possible signal…
The final step of most large-scale structure analyses involves the comparison of power spectra or correlation functions to theoretical models. It is clear that the theoretical models have parameter dependence, but frequently the…
A common problem in numerous research areas, particularly in clinical trials, is to test whether the effect of an explanatory variable on an outcome variable is equivalent across different groups. In practice, these tests are frequently…
The comparison of a parameter in $k$ populations is a classical problem in statistics. Testing for the equality of means or variances are typical examples. Most procedures designed to deal with this problem assume that $k$ is fixed and that…
In this manuscript we consider random objects being measured in multiple metric spaces, which may arise when those objects may be measured in multiple distinct ways. In this new multivariate setting, we define a Fr\'echet covariance and…
Testing for change points in sequences of covariance matrices is an important and equally challenging problem in statistical methodology with applications in various fields. Motivated by the observation that even in cases where the ratio…
Statistical models that possess symmetry arise in diverse settings such as random fields associated to geophysical phenomena, exchangeable processes in Bayesian statistics, and cyclostationary processes in engineering. We formalize the…
Joint modeling of a large number of variables often requires dimension reduction strategies that lead to structural assumptions of the underlying correlation matrix, such as equal pair-wise correlations within subsets of variables. The…
This paper studies methods for testing and estimating change-points in the covariance structure of a high-dimensional linear time series. The assumed framework allows for a large class of multivariate linear processes (including vector…
We examine the extent to which sublinear-sample property testing and estimation apply to settings where samples are independently but not identically distributed. Specifically, we consider the following distributional property testing…
The covariance of two random variables measures the average joint deviations from their respective means. We generalise this well-known measure by replacing the means with other statistical functionals such as quantiles, expectiles, or…
This paper proposes a new mutual independence test for a large number of high dimensional random vectors. The test statistic is based on the characteristic function of the empirical spectral distribution of the sample covariance matrix. The…
In this paper, a robust non-parametric measure of statistical dependence, or correlation, between two random variables is presented. The proposed coefficient is a permutation-like statistic that quantifies how much the observed sample S_n :…
In this paper, we obtain a new characterization result for symmetric distributions based on the entropy measure. Using the characterization, we propose a nonparametric test to test the symmetry of a distribution. We also develop the…
Determining the relevant spatial covariates is one of the most important problems in the analysis of point patterns. Parametric methods may lead to incorrect conclusions, especially when the model of interactions between points is wrong.…
We propose a new asymptotic test for the separability of a covariance matrix. The null distribution is valid in wide matrix elliptical model that includes, in particular, both matrix Gaussian and matrix $t$-distribution. The test is fast to…
Modeling correlation (and covariance) matrices can be challenging due to the positive-definiteness constraint and potential high-dimensionality. Our approach is to decompose the covariance matrix into the correlation and variance matrices…
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…
Understanding causal relationships among the variables of a system is paramount to explain and control its behavior. For many real-world systems, however, the true causal graph is not readily available and one must resort to predictions…
High-dimensional vector autoregression with measurement error is frequently encountered in a large variety of scientific and business applications. In this article, we study statistical inference of the transition matrix under this model.…