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The extension of bivariate measures of dependence to non-Euclidean spaces is a challenging problem. The non-linear nature of these spaces makes the generalisation of classical measures of linear dependence (such as the covariance) not…

Statistics Theory · Mathematics 2024-10-10 Meshal Abuqrais , Davide Pigoli

A random coefficient autoregressive process is deeply investigated in which the coefficients are correlated. First we look at the existence of a strictly stationary causal solution, we give the second-order stationarity conditions and the…

Statistics Theory · Mathematics 2018-03-29 Frédéric Proïa , Marius Soltane

The distribution function of a random distance in three dimensions is given and some new three-dimensional d2-tests of randomness are suggested. We show that our test statistics are not correlated with the usual test statistics and are…

Applications · Statistics 2014-02-24 Sergii Koliada

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…

Methodology · Statistics 2017-09-20 Shun Yao , Xianyang Zhang , Xiaofeng Shao

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…

Methodology · Statistics 2026-01-28 Jinyuan Chang , Yue Du , Jing He , Qiwei Yao

We are concerned with the detection of associations between random vectors of any dimension. Few tests of independence exist that are consistent against all dependent alternatives. We propose a powerful test that is applicable in all…

Methodology · Statistics 2013-08-08 Ruth Heller , Yair Heller , Malka Gorfine

The paper contains results in three areas: First we present a general estimate for tail probabilities of Gaussian quadratic forms with known expectation and variance. Thereafter we analyze the distribution of norms of complex Gaussian…

Probability · Mathematics 2019-03-20 Georg Berschneider , Björn Böttcher

In this article, we study tests of independence for data with arbitrary distributions in the non-serial case, i.e., for independent and identically distributed random vectors, as well as in the serial case, i.e., for time series. These…

Methodology · Statistics 2023-06-13 Bouchra R. Nasri , Bruno N. Remillard

The use of empirical characteristic functions for inference problems, including estimation in some special parametric settings and testing for goodness of fit, has a long history dating back to the 70s (see for example, Feuerverger and…

Statistics Theory · Mathematics 2016-06-20 Richard A. Davis , Muneya Matsui , Thomas Mikosch , Phyllis Wan

The coefficient of variation is a useful indicator for comparing the spread of values between dataset with different units or widely different means. In this paper we address the problem of investigating the equality of the coefficients of…

Methodology · Statistics 2023-06-06 Francesco Bertolino , Silvia Columbu , Mara Manca , Monica Musio

Measuring a strength of dependence of random variables is an important problem in statistical practice. In this paper, we propose a new function valued measure of dependence of two random variables. It allows one to study and visualize…

Methodology · Statistics 2014-05-12 Teresa Ledwina

Log-Euclidean distances are commonly used to quantify the similarity between positive definite matrices using geometric considerations. This paper analyzes the behavior of this distance when it is used to measure closeness between…

Signal Processing · Electrical Eng. & Systems 2024-08-09 Xavier Mestre , Roberto Pereira

In many statistical modeling frameworks, goodness-of-fit tests are typically administered to the estimated residuals. In the time series setting, whiteness of the residuals is assessed using the sample autocorrelation function. For many…

Statistics Theory · Mathematics 2019-03-05 Phyllis Wan , Richard A. Davis

In this paper we propose several variants to perform the independence test between two random elements based on recurrence rates. We will show how to calculate the test statistic in each one of these cases. From simulations we obtain that…

Methodology · Statistics 2020-09-21 Juan Kalemkerian , Diego Fernández

To quantify the dependence between two random vectors of possibly different dimensions, we propose to rely on the properties of the 2-Wasserstein distance. We first propose two coefficients that are based on the Wasserstein distance between…

Statistics Theory · Mathematics 2021-10-19 Gilles Mordant , Johan Segers

A dependence measure for arbitrary type pairs of random variables is proposed and analyzed, which in the particular case where both random variables are continuous turns out to be a concordance measure. Also, a sample version of the…

Statistics Theory · Mathematics 2017-02-07 Arturo Erdely

We begin with an interpretation of the L1-distance between two power spectral densities and then, following an analogous rationale, we develop a natural metric for quantifying distance between respective covariance matrices.

Optimization and Control · Mathematics 2007-06-13 Tryphon T. Georgiou

Given well-shuffled data, can we determine whether the data items are statistically (in)dependent? Formally, we consider the problem of testing whether a set of exchangeable random variables are independent. We will show that this is…

Statistics Theory · Mathematics 2022-10-25 Marcus Hutter

The partial correlation coefficient is a commonly used measure to assess the conditional dependence between two random variables. We provide a thorough explanation of the partial copula, which is a natural generalization of the partial…

Methodology · Statistics 2017-06-13 Fabian Spanhel , Malte S. Kurz

We propose and analyze a specific asymptotic stochastic order for random processes based on the measure of departure discussed in the literature. As applications, we stochastically compare mixtures of order statistics and record values…

Probability · Mathematics 2021-03-04 Sugata Ghosh , Asok K. Nanda