Related papers: Generalized R-squared for Detecting Dependence
Multivariate time series anomaly detection has numerous real-world applications and is being extensively studied. Modeling pairwise correlations between variables is crucial. Existing methods employ learnable graph structures and graph…
Chi-squared tests for lack of fit are traditionally employed to find evidence against a hypothesized model, with the model accepted if the Karl Pearson statistic comparing observed and expected numbers of observations falling within cells…
Testing for dependence has been a well-established component of spatial statistical analyses for decades. In particular, several popular test statistics have desirable properties for testing for the presence of spatial autocorrelation in…
The $X^2$ and $G^2$ tests are the most frequently applied tests for testing the independence of two categorical variables. However, no one, to the best of our knowledge has compared them, extensively, and ultimately answer the question of…
In this paper, we study change-point testing for high-dimensional linear models, an important problem that has not been well explored in the literature. Specifically, we propose a quadratic-form cumulative sum (CUSUM) statistic to test the…
In this paper, we introduce quantile coherency to measure general dependence structures emerging in the joint distribution in the frequency domain and argue that this type of dependence is natural for economic time series but remains…
A new family of nonparametric statistics, the r-statistics, is introduced. It consists of counting the number of records of the cumulative sum of the sample. The single-sample r-statistic is almost as powerful as Student's t-statistic for…
In this paper, we study distance covariance, Hilbert-Schmidt covariance (aka Hilbert-Schmidt independence criterion [Gretton et al. (2008)]) and related independence tests under the high dimensional scenario. We show that the sample…
Multivariate correlation analysis plays a key role in various fields such as statistics and big data analytics. In this paper, it is presented a new non-parametric association measure between more than two variables based on the concept of…
In this paper we study the asymptotics of linear regression in settings with non-Gaussian covariates where the covariates exhibit a linear dependency structure, departing from the standard assumption of independence. We model the covariates…
Testing mutual independence for high-dimensional observations is a fundamental statistical challenge. Popular tests based on linear and simple rank correlations are known to be incapable of detecting non-linear, non-monotone relationships,…
Distance covariance is a popular measure of dependence between random variables. It has some robustness properties, but not all. We prove that the influence function of the usual distance covariance is bounded, but that its breakdown value…
The quotient correlation is defined here as an alternative to Pearson's correlation that is more intuitive and flexible in cases where the tail behavior of data is important. It measures nonlinear dependence where the regular correlation…
We introduce a new procedure for testing the significance of a set of regression coefficients in a Gaussian linear model with $n \geq d$. Our method, the $L$-test, provides the same statistical validity guarantee as the classical $F$-test,…
In this paper new tests for the independence of two high-dimensional vectors are investigated. We consider the case where the dimension of the vectors increases with the sample size and propose multivariate analysis of variance-type…
The categorical Gini correlation is an alternative measure of dependence between a categorical and numerical variables, which characterizes the independence of the variables. A nonparametric test for the equality of K distributions has been…
This paper proposes a new statistic to test independence between two high dimensional random vectors ${\mathbf{X}}:p_1\times1$ and ${\mathbf{Y}}:p_2\times1$. The proposed statistic is based on the sum of regularized sample canonical…
Conditional independence testing is a key problem required by many machine learning and statistics tools. In particular, it is one way of evaluating the usefulness of some features on a supervised prediction problem. We propose a novel…
Model selection for Gaussian concentration graph is based on multiple testing of pairwise conditional independence. In practical applications partial correlation tests are widely used. However it is not known whether partial correlation…
Understanding the relationships between different properties of data, such as whether a connectome or genome has information about disease status, is becoming increasingly important in modern biological datasets. While existing approaches…