DeepAI AI Chat
Log In Sign Up

Ridge-type Linear Shrinkage Estimation of the Matrix Mean of High-dimensional Normal Distribution

10/26/2019
by   Ryota Yuasa, et al.
0

The estimation of the mean matrix of the multivariate normal distribution is addressed in the high dimensional setting. Efron-Morris-type linear shrinkage estimators based on ridge estimators for the precision matrix instead of the Moore-Penrose generalized inverse are considered, and the weights in the ridge-type linear shrinkage estimators are estimated in terms of minimizing the Stein unbiased risk estimators under the quadratic loss. It is shown that the ridge-type linear shrinkage estimators with the estimated weights are minimax, and that the estimated weights converge to the optimal weights in the Bayesian model with high dimension by using the random matrix theory. The performance of the ridge-type linear shrinkage estimators is numerically compared with the existing estimators including the Efron-Morris and James-Stein estimators.

READ FULL TEXT

page 1

page 2

page 3

page 4

07/29/2021

Polynomials shrinkage estimators of a multivariate normal mean

In this work, the estimation of the multivariate normal mean by differen...
02/27/2020

Tuning-free ridge estimators for high-dimensional generalized linear models

Ridge estimators regularize the squared Euclidean lengths of parameters....
06/07/2015

Optimal Ridge Detection using Coverage Risk

We introduce the concept of coverage risk as an error measure for densit...
08/14/2016

The Spectral Condition Number Plot for Regularization Parameter Determination

Many modern statistical applications ask for the estimation of a covaria...
10/15/2020

Mean Shrinkage Estimation for High-Dimensional Diagonal Natural Exponential Families

Shrinkage estimators have been studied widely in statistics and have pro...
12/13/2018

Split regression modeling

In this note we study the benefits of splitting variables variables for ...