Empirical Bayes estimation in continuous one-parameter exponential families under associated samples

In this paper, we study the empirical Bayes (EB) estimation in continuous one-parameter exponential families under negatively associated (NA) samples and positively associated (PA) samples. Under certain regularity conditions, it is shown that the convergence rates of proposed EB estimators under NA or PA samples are the same as those of EB estimators under independent observations, which significantly improve the existing results in EB estimation under associated samples.