Related papers: A test for normality and independence based on cha…
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…
The asymptotic normality for a large family of eigenvalue statistics of a general sample covariance matrix is derived under the ultra-high dimensional setting, that is, when the dimension to sample size ratio $p/n \to \infty$. Based on this…
In the common time series model $X_{i,n} = \mu (i/n) + \varepsilon_{i,n}$ with non-stationary errors we consider the problem of detecting a significant deviation of the mean function $\mu$ from a benchmark $g (\mu )$ (such as the initial…
This paper introduces an extension to the normal distribution through the polar method to capture bimodality and asymmetry, which are often observed characteristics of empirical data. The later two features are entirely controlled by a…
Conditional independence (CI) testing arises naturally in many scientific problems and applications domains. The goal of this problem is to investigate the conditional independence between a response variable $Y$ and another variable $X$,…
We investigate the problem of testing whether $d$ random variables, which may or may not be continuous, are jointly (or mutually) independent. Our method builds on ideas of the two variable Hilbert-Schmidt independence criterion (HSIC) but…
The paper discusses a test for the hypothesis that a random sample comes from the Cauchy distribution. The test statistics is derived from a characterization and is based on the characteristic function. Properties of the test are discussed…
Measurements of systems taken along a continuous functional dimension, such as time or space, are ubiquitous in many fields, from the physical and biological sciences to economics and engineering.Such measurements can be viewed as…
This paper proposes a novel test method for high-dimensional mean testing regard for the temporal dependent data. Comparison to existing methods, we establish the asymptotic normality of the test statistic without relying on restrictive…
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…
We treat the problem of testing independence between m continuous variables when m can be larger than the available sample size n. We consider three types of test statistics that are constructed as sums or sums of squares of pairwise rank…
We consider the conditional randomization test as a way to account for covariate imbalance in randomized experiments. The test accounts for covariate imbalance by comparing the observed test statistic to the null distribution of the test…
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 establishes the asymptotic independence between the quadratic form and maximum of a sequence of independent random variables. Based on this theoretical result, we find the asymptotic joint distribution for the quadratic form and…
It is known that if X is uniformly distributed modulo 1 and Y is an arbitrary random variable independent of X then Y+X is also uniformly distributed modulo 1. We prove a converse for any continuous random variable Y (or a reasonable…
We show that one single experiment can test simultaneously and independently both the nonclassicality of states and measurements by the violation or fulfillment of classical bounds on the statistics. Nonideal measurements affected by…
This paper is concerned with testing normality in a Hilbert space based on the maximum mean discrepancy. Specifically, we discuss the behavior of the test from two standpoints: asymptotics and practical aspects. Asymptotic normality of the…
We propose the density ratio permutation test, a hypothesis test that assesses whether the ratio between two densities is proportional to a known function based on independent samples from each distribution. The test uses an efficient…
We propose two families of tests for the classical goodness-of-fit problem to univariate normality. The new procedures are based on $L^2$-distances of the empirical zero-bias transformation to the normal distribution or the empirical…
Testing conditional independence between two random vectors given a third is a fundamental and challenging problem in statistics, particularly in multivariate nonparametric settings due to the complexity of conditional structures. We…