Related papers: Kendall's Tau for Functional Data Analysis
Hypothesis testing in high dimensional data is a notoriously difficult problem without direct access to competing models' likelihood functions. This paper argues that statistical divergences can be used to quantify the difference between…
To detect differences between the mean curves of two samples in longitudinal study or functional data analysis, we usually need to partition the temporal or spatial domain into several pre-determined sub-areas. In this paper we apply the…
We consider the problem of similarity search within a set of top-k lists under the Kendall's Tau distance function. This distance describes how related two rankings are in terms of concordantly and discordantly ordered items. As top-k lists…
We consider the problem of consistently estimating the conditional distribution $P(Y \in A |X)$ of a functional data object $Y=(Y(t): t\in[0,1])$ given covariates $X$ in a general space, assuming that $Y$ and $X$ are related by a functional…
Let $\{S_n=(X_n,W_n)\}_{n\ge0}$ be a random walk with $X_n\in \mathbb{R}$ and $W_n\in \mathbb{R}^m$. Let $\tau=\tau_a=\inf\{n:X_n>a\}$. The main results presented are two term asymptotic expansions for the joint distribution of $S_{\tau}$…
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…
Sphericity test plays a key role in many statistical problems. We propose Spearman's rho-type rank test and Kendall's tau-type rank test for sphericity in the high dimensional settings. We show that these two tests are equivalent. Thanks to…
In this paper, we are concerned with the independence test for $k$ high-dimensional sub-vectors of a normal vector, with fixed positive integer $k$. A natural high-dimensional extension of the classical sample correlation matrix, namely…
This paper presents new results on Functional Analysis of Variance for fixed effect models with correlated Hilbert-valued Gaussian error components. The geometry of the Reproducing Kernel Hilbert Space (RKHS) of the error term is considered…
We introduce the coverage correlation coefficient, a novel nonparametric measure of statistical association designed to quantifies the extent to which two random variables have a joint distribution concentrated on a singular subset with…
The paper considers a paired data framework and discuss the question of marginal homogeneity of bivariate high dimensional or functional data. The related testing problem can be endowed into a more general setting for paired random…
We consider settings in which the data of interest correspond to pairs of ordered times, e.g, the birth times of the first and second child, the times at which a new user creates an account and makes the first purchase on a website, and the…
Temporal data are increasingly prevalent in modern data science. A fundamental question is whether two time series are related or not. Existing approaches often have limitations, such as relying on parametric assumptions, detecting only…
Every copula $ C $ for a random vector $ {\bf X}=(X_1,\dots,X_d) $ with identically distributed coordinates determines a unique copula $ C_{:d} $ for its order statistic $ {\bf X}_{:d}=(X_{1:d},\dots,X_{d:d}) $. In the present paper we…
We introduce a correlation coefficient that is designed to deal with a variety of ranking formats including those containing non-strict (i.e., with-ties) and incomplete (i.e., unknown) preferences. The correlation coefficient is designed to…
We propose a novel family of test statistics to detect the presence of changepoints in a sequence of dependent, possibly multivariate, functional-valued observations. Our approach allows to test for a very general class of changepoints,…
Motivated by the importance of measuring the association between the response and predictors in high dimensional data, In this article, we propose a new mean variance test of independence between a categorical random variable and a…
We consider the problem of testing whether two finite-dimensional random dot product graphs have generating latent positions that are independently drawn from the same distribution, or distributions that are related via scaling or…
In applications like environment monitoring and pollution control, physical quantities are modeled by spatio-temporal fields. It is of interest to learn the statistical distribution of such fields as a function of space, time or both. In…
The Gaussian graphical model is routinely employed to model the joint distribution of multiple random variables. The graph it induces is not only useful for describing the relationship between random variables but also critical for…