Empirical Bayes and Conditional Inference with Many Nuisance Parameters
研究在存在大量冗余参数时，如何用经验贝叶斯方法提高目标参数的估计效率，提出一类分布并证明条件得分函数的最优性，通过模拟比较三种估计方法。
This paper concerns the use of empirical Bayes methods to improve the efficiency of a parameter of interest, θ, in the presence of many nuisance parameters, {øi}, one from each data stratum. A class of distributions is introduced such that for fixed θ, the minimal sufficient statistic ti(θ) for øi is from an exponential family and hence complete. By imposing the assumption that the øi's are generated from an unspecified distribution function Q, we show that for this class of distributions the conditional score function for θ (Lindsay, 1982) with oslhasi estimated by EQ{oslhasi /ti(θ)} is optimal in a sense similar to that of Cox & Reid (1987) and Liang (1987). Two empirical Bayes estimates of ø, along with the maximum likelihood estimate of øi are compared through simulations in terms of θ estimation.