Zhigen Zhao
Associate Professor
Department of Statistical Science
Center for Data Analytics and Biomedical Informatics
Temple University
Nonparametric Empirical Bayes Estimator For
Simultaneous Variances
Abstract
The shrinkage estimation has proven to be very useful when facing with a large number of mean parameters to be estimated. In the modern application, we also face with the situation of estimating a large number of variances simultaneously. There are a few attempts to introduce the shrinkage variance estimators using parametric empirical Bayes approach.
In this paper, we construct a non-parametric estimation of simultaneous variances (NESV). Namely, we take the f-modeling approach and assume an arbitrary prior on the variances. Under an invariant loss function, the resultant Bayes decision estimator relies on the marginal cumulative distribution function only, which can be reliably estimated using the empirical distribution function.
We applied the proposed NESV to construct the confidence intervals for the (selected) mean parameters. It is shown that the intervals based on the NESV are shortest among all the intervals which guarantee a desired coverage probability. Through two real data analysis, we have further shown that the NESV based intervals lead to the smallest number of discordant parameters, a favorable property when facing with the current “replication crisis”.
DATE: Wednesday, November 15, 2017
TIME: 4:00 pm
PLACE: Philip E. Austin Bldg., Rm. 105
Coffee will be served at 3:30 pm in the Noether Lounge (AUST 326)
For more information, contact: Tracy Burke at tracy.burke@uconn.edu