title: OPTIMAL SHRINKAGE ESTIMATION OF MEAN PARAMETERS IN FAMILY OF DISTRIBUTIONS WITH QUADRATIC VARIANCE.
abstract: This paper discusses the simultaneous inference of mean parameters in a family of distributions with quadratic variance function. We first introduce a class of semi-parametric/parametric shrinkage estimators and establish their asymptotic optimality properties. Two specific cases, the location-scale family and the natural exponential family with quadratic variance function, are then studied in detail. We conduct a comprehensive simulation study to compare the performance of the proposed methods with existing shrinkage estimators. We also apply the method to real data and obtain encouraging results.
authors.affiliation: Two Sigma Investments LLC, 100 Avenue of the Americas, Floor 16, New York, NY 10013, xie1981@gmail.com.
authors.forename: Xianchao
authors.initials: X
authors.lastname: Xie
authors.affiliation: Department of Statistics, Harvard University, Cambridge, MA 02138, kou@stat.harvard.edu.
authors.forename: S C
authors.initials: SC
authors.lastname: Kou
authors.affiliation: The Wharton School, University of Pennsylvania, Philadelphia, PA 19104, lbrown@wharton.upenn.edu.
authors.forename: Lawrence
authors.initials: L
authors.lastname: Brown
keywords: NEF-QVF; asymptotic optimality; hierarchical model; location-scale family; quadratic variance function; shrinkage estimator; unbiased estimate of risk