Related papers: Kendall's Tau for Functional Data Analysis
We take a different look at the problem of testing the independence of two metric-space-valued random variables using the distance correlation. Instead of testing if the distance correlation vanishes exactly, we are interested in the…
While there exists several inferential methods for analyzing functional data in factorial designs, there is a lack of statistical tests that are valid (i) in general designs, (ii) under non-restrictive assumptions on the data generating…
In this work, we introduce statistical testing under distributional shifts. We are interested in the hypothesis $P^* \in H_0$ for a target distribution $P^*$, but observe data from a different distribution $Q^*$. We assume that $P^*$ is…
Introduction The tau statistic is a recent second-order correlation function that can assess the magnitude and range of global spatiotemporal clustering from epidemiological data containing geolocations of individual cases and, usually,…
ANOVA decomposition of function with random input variables provides ANOVA functionals (AFs), which contain information about the contributions of the input variables on the output variable(s). By embedding AFs into an appropriate…
We propose a novel statistical test to assess the mutual independence of multidimensional random vectors. Our approach is based on the $L_1$-distance between the joint density function and the product of the marginal densities associated…
Functional data that are nonnegative and have a constrained integral can be considered as samples of one-dimensional density functions. Such data are ubiquitous. Due to the inherent constraints, densities do not live in a vector space and,…
This paper focuses on a data-rich environment where the data set has a very large cross-sectional dimension, is likely to exhibit local dependence, and yet is hard to determine the dependence ordering. Such a situation arises, for example,…
We revisit the classical problem of comparing regression functions, a fundamental question in statistical inference with broad relevance to modern applications such as data integration, transfer learning, and causal inference. Existing…
The problem of testing for the parametric form of the conditional variance is considered in a fully nonparametric regression model. A test statistic based on a weighted $L_2$-distance between the empirical characteristic functions of…
We introduce the Statistical Asynchronous Regression (SAR) method: a technique for determining a relationship between two time varying quantities without simultaneous measurements of both quantities. We require that there is a time…
Many high-dimensional hypothesis tests aim to globally examine marginal or low-dimensional features of a high-dimensional joint distribution, such as testing of mean vectors, covariance matrices and regression coefficients. This paper…
In competing risks models, cumulative incidence functions are commonly compared to infer differences between groups. Many existing inference methods, however, struggle when these functions cross during the time frame of interest. To address…
Most of the popular dependence measures for two random variables $X$ and $Y$ (such as Pearson's and Spearman's correlation, Kendall's $\tau$ and Gini's $\gamma$) vanish whenever $X$ and $Y$ are independent. However, neither does a vanishing…
We introduce a new type of test for complete spatial randomness that applies to mapped point patterns in a rectangle or a cube of any dimension. This is the first test of its kind to be based on characteristic functions and utilizes a…
In this paper, we focus on the problem of stable prediction across unknown test data, where the test distribution is agnostic and might be totally different from the training one. In such a case, previous machine learning methods might…
As a rigorous statistical approach, statistical Taylor expansion extends the conventional Taylor expansion by replacing precise input variables with random variables of known distributions and sample counts to compute the mean, the…
Testing for association or dependence between pairs of random variables is a fundamental problem in statistics. In some applications, data are subject to selection bias that causes dependence between observations even when it is absent from…
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…
For hypothesis testing of functional parameters, given a functional statistic $T_n$ and a functional depth $D$ with respect to the distribution $P_n$ of $T_n$, we propose the depth value $DT_n \equiv D(T_n;P_n)$ as a test statistic, which…