A nonparametric test for the change of the density function in strong mixing processes

In this paper, we consider the problem of testing for a change of the marginal density of a strong mixing process. The test statistic is constructed based on the sequential kernel estimate. In order to derive the asymptotic distribution of the test statistic, we first show that a functional central limit theorem holds for the sequential density estimator under some regularity conditions. Based on the result, we show that the limiting distribution of the test statistic is a function of independent Brownian bridges.