A nonparametric test for the change of the density function under association

Abstract

In this paper, we consider the problem of testing for a change of the marginal density of a strictly stationary sequence Xn, n≥1, which is either associated or negatively associated. The test statistic is constructed based on the sequential kernel estimate of the density function. We first establish a functional central limit theorem for the kernel density estimator under appropriate conditions. Then, we show that the limiting distribution of the test statistic is a functional of independent Brownian bridges.