A0978
Title: A nonparametric integrative Tweedie approach to empirical Bayes estimation with side information
Authors: Wenguang Sun - Zhejiang University (China) [presenting]
Abstract: Compound estimation of normal means with auxiliary data collected from related source domains is considered. The empirical Bayes framework provides an elegant interface to pool information across different samples and construct efficient shrinkage estimators. We propose a nonparametric integrative Tweedie (NIT) approach to incorporating structural knowledge encoded in the auxiliary data to assist the simultaneous estimation of primary vector of parameters. NIT uses convex optimization tools to directly estimate the gradient of the log-density through an embedding in the reproducing kernel Hilbert space (RKHS), which is induced by the Steins discrepancy metric. Most popular structural constraints can be easily incorporated into our estimation framework. We characterize the asymptotic Lp risk of NIT by first rigorously analyzing its connections to the RKHS risk, and second establishing the rate at which NIT converges to the oracle estimator. The improvements in the estimation risk and the deteriorations in the learning rate are precisely tabulated as the dimension of side information grows. The numerical performance of NIT and its superiority over existing methods are illustrated through the analysis of both simulated and real data.
