The uniformly strong consistency of kernel-type distribution estimator under asymptotically almost negatively associated samples

Abstract

This paper studies the kernel-type distribution estimator based on asymptotically almost negatively associated (AANA, for short) samples. The rate of uniformly strong consistency is established under some mild conditions. As applications, the uniformly strong convergence rates of kernel-type density estimator and kernel-type hazard rate estimator are also obtained. Some Monte Carlo simulations are presented to illustrate the finite sample performance of the kernel method. Finally, a real data analysis of Alibaba stock returns data is used to illustrate the usefulness of the proposed methodology.

Keywords

• Kernel-type distribution estimator
• uniformly strong consistency
• AANA sequences