統計学輪講（第20回）


日時	2018年11月20日（火） 14時55分～ 15時45分
場所	経済学研究科棟 3階第3教室
講演者	Wang Zeyu （情報理工学系研究科M2）
演題	Shape constraint approaches for Gaussian noise model estimation （文献紹介）
概要	Estimation of mixture densities for the classical Gaussian compound decision problem and their associated nonparametric (empirical) Bayes rules is considered from two new perspectives. One is motivated by Brown and Greenshtein [1] and another is motivated by Jiang and Zhang [2]. In the paper that will be introduced [3], the authors apply shape constraint method to both approaches and the estimation problems are transformed to convex optimization problems that can be efficiently solved by modern interior point methods. (And it is possible that some other shape constraint topics will also be introduced briefly.) 参考文献 [1] Brown, L. D., & Greenshtein, E. (2009). Nonparametric empirical Bayes and compound decision approaches to estimation of a high-dimensional vector of normal means. The Annals of Statistics, 1685–1704. [2] Jiang, W., & Zhang, C. H. (2009). General maximum likelihood empirical Bayes estimation of normal means. The Annals of Statistics, 37(4), 1647–1684. [3]Koenker, R., & Mizera, I. (2014). Convex optimization, shape constraints, compound decisions, and empirical Bayes rules. Journal of the American Statistical Association, 109(506), 674–685.