Bahadur exact slopes of some tests for spectral densities

摘要

The large deviation result is proved for two functionals of the empirical spectral process in zero-mean Gaussian stationary processes. As a statistical application, we deal with the Bahadur asymptotic efficiencies of two statistics for testing H: f_1 = f (specified), which are spectral analogue to the Kolmogorov-Smirnov (KS) and Kuiper statistics for testing hypothesis about distribution function in the iid setting. It is shown that the Kuiper type statistic is superior to the KS type statistic in terms of the Bahadur exact slope. We also discuss the a ( ≥ 2)-sample problem. Especially, for the two-sample problem, we investigate the Bahadur asymptotic efficiencies of several statistics for testing not only the goodness-of-fit hypothesis H_1: f_1 = f_2 = f (specified) but also the homogeneity hypothesis H_2 : f_1 = f_2 (unspecified).