Asymptotic Independence of the Quadratic Form and Maximum of Independent Random Variables with Applications to High-Dimensional Tests

This paper establishes the asymptotic independence between the quadratic form z^(T)Az and maximum max1≤i≤p|zi|of a sequence of independent sub-Gaussian random variables z=(z1m…zp)^(T).Based on this theoretical result,we find the asymptotic joint distribution for the quadratic form and maximum,which can be applied into the high-dimensional testing problems.By combining the sum-type test and the max-type test,we propose the Fisher’s combination tests for the one-sample mean test and two-sample mean test.Under this novel general framework,several strong assumptions in existing literature have been relaxed.Monte Carlo simulation has been done which shows that our proposed tests are strongly robust to both sparse and dense data.

Uniform Asymptotics for Finite-time Ruin Probability in a Dependent Risk Model with General Stochastic Investment Return Process

In this paper,we consider a non-standard renewal risk model with dependent claim sizes,where an insurance company is allowed to invest his/her wealth in financial assets,leading to some stochastic investment log-returns described as a general adapted càdlàg process.Under the assumptions that the claim sizes are heavy-tailed and the stochastic log-return process on investments is bounded from below almost surely,we derive some asymptotic formulas for the finite-time ruin probability holding uniformly in any finite time horizon.

Uniform Estimate for The Tail Probabilities of Randomly Weighted Sums

Several authors have studied the uniform estimate for the tail probabilities of randomly weighted sumsa.ud their maxima. In this paper, we generalize their work to the situation thatis a sequence of upper tail asymptotically independent random variables with common distribution from the is a sequence of nonnegative random variables, independent of and satisfying some regular conditions. Moreover. no additional assumption is required on the dependence structureof {θi,i≥ 1）.

On the asymptotic independence of the sum and maximum of normal random variables

RECENTLY, a number of papers have been published concerning the asymptotic independentproperties of V Xi and sum from 1 Xi of weakly dependent stationary sequence {Xi}.In this letter, let {Xi} be a standard normal sequence of random variables with zero meanand unit variance and write rij=cov（Xi, Xj）.

A note on testing conditional independence for social network analysis

In social network analysis, logistic regression models have been widely used to establish the relationship between the response variable and covariates. However, such models often require the network relationships to be mutually independent, after controlling for a set of covariates. To assess the validity of this assumption,we propose test statistics, under the logistic regression setting, for three important social network drivers. They are, respectively, reciprocity, centrality, and transitivity. The asymptotic distributions of those test statistics are obtained. Extensive simulation studies are also presented to demonstrate their finite sample performance and usefulness.