Related papers: Kendall's Tau for Functional Data Analysis
Functional principal component analysis is essential in functional data analysis, but the inferences will become unconvincing when some non-Gaussian characteristics occur, such as heavy tail and skewness. The focus of this paper is to…
In this article, we study the test for independence of two random elements $X$ and $Y$ lying in an infinite dimensional space ${\cal{H}}$ (specifically, a real separable Hilbert space equipped with the inner product $\langle .,…
We consider linear models with scalar responses and covariates from a separable Hilbert space. The aim is to detect change points in the error distribution, based on sequential residual empirical distribution functions. Expansions for those…
One of the most popular class of tests for independence between two random variables is the general class of rank statistics which are invariant under permutations. This class contains Spearman's coefficient of rank correlation statistic,…
Large-dimensional factor model has drawn much attention in the big-data era, in order to reduce the dimensionality and extract underlying features using a few latent common factors. Conventional methods for estimating the factor model…
For a random variable $X$, we are interested in the blind extraction of its finest mutual independence pattern $\mu ( X )$. We introduce a specific kind of independence that we call dichotomic. If $\Delta ( X )$ stands for the set of all…
In this article, we show that the recently introduced ordinal pattern dependence fits into the axiomatic framework of general multivariate dependence measures, i.e., measures of dependence between two multivariate random objects.…
Mobile health studies often collect multiple within-day self-reported assessments of participants' behavior and well-being on different scales such as physical activity (continuous), pain levels (truncated), mood states (ordinal), and life…
The need to test whether two random vectors are independent has spawned a large number of competing measures of dependence. We are interested in nonparametric measures that are invariant under strictly increasing transformations, such as…
For a set of dependent random variables, without stationary or the strong mixing assumptions, we derive the asymptotic independence between their sums and maxima. Then we apply this result to high-dimensional testing problems, where we…
Mathematical formulations and proofs for a wavelet based statistic employed in functional data analysis is elaborately discussed in this report. The propositions and derivations discussed here apply to a wavelet based statistic with hard…
The rapid development of modern technology facilitates the appearance of numerous unprecedented complex data which do not satisfy the axioms of Euclidean geometry, while most of the statistical hypothesis tests are available in Euclidean or…
This paper is concerned with test of the conditional independence. We first establish an equivalence between the conditional independence and the mutual independence. Based on the equivalence, we propose an index to measure the conditional…
Understanding the correlation between two different scores for the same set of items is a common problem in information retrieval, and the most commonly used statistics that quantifies this correlation is Kendall's $\tau$. However, the…
Energy statistics are estimators of the energy distance that depend on the distances between observations. The idea behind energy statistics is to consider a statistical potential energy that would parallel Newton's gravitational potential…
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…
A new procedure is presented, which allows, based on Kendall's $\tau$, to test for partial correlation in the presence of censored data. Further, a significance level can be assigned to the partial correlation -- a problem which hasn't been…
Conditional independence is a fundamental concept in many areas of statistical research, including, for example, sufficient dimension reduction, causal inference, and statistical graphical models. In many modern applications, data arise in…
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…
Identifying how dependence relationships vary across different conditions plays a significant role in many scientific investigations. For example, it is important for the comparison of biological systems to see if relationships between…