Regularized parameter estimation of high dimensional t distribution |
| |
Authors: | Ming Yuan Jianhua Z Huang |
| |
Institution: | 1. School of Industrial and Systems Engineering, Georgia Institute of Technology, 755 Ferst Drive NW, Atlanta, GA 30332, USA;2. Department of Statistics, Texas A&M University, 3143 TAMU, College Station, TX 77843, USA |
| |
Abstract: | We propose penalized-likelihood methods for parameter estimation of high dimensional t distribution. First, we show that a general class of commonly used shrinkage covariance matrix estimators for multivariate normal can be obtained as penalized-likelihood estimator with a penalty that is proportional to the entropy loss between the estimate and an appropriately chosen shrinkage target. Motivated by this fact, we then consider applying this penalty to multivariate t distribution. The penalized estimate can be computed efficiently using EM algorithm for given tuning parameters. It can also be viewed as an empirical Bayes estimator. Taking advantage of its Bayesian interpretation, we propose a variant of the method of moments to effectively elicit the tuning parameters. Simulations and real data analysis demonstrate the competitive performance of the new methods. |
| |
Keywords: | EM algorithm Empirical Bayes Multivariate t distribution Penalized likelihood |
本文献已被 ScienceDirect 等数据库收录! |
|