On some inequalities for ψ-mixing sequences and its applications in conditional value-at-risk estimate

摘要

In this paper, we present an inequality of characteristic functions for psi-mixing random vectors, and derive an upper bound for the supremum of the absolute value of the difference of two multivariate probability density functions based on psi-mixing random vectors. For its application, we discuss the Berry-Esseen type bounds for conditional value-at-risk estimator based on psi-mixing sequences, by the suitable choice of some constants, the Berry-Esseen type bounds of the estimator can attain O(n(-1/6)).