The Annals of Statistics
- Ann. Statist.
- Volume 33, Number 4 (2005), 1753-1770.
A new class of generalized Bayes minimax ridge regression estimators
Let y=Aβ+ɛ, where y is an N×1 vector of observations, β is a p×1 vector of unknown regression coefficients, A is an N×p design matrix and ɛ is a spherically symmetric error term with unknown scale parameter σ. We consider estimation of β under general quadratic loss functions, and, in particular, extend the work of Strawderman [J. Amer. Statist. Assoc. 73 (1978) 623–627] and Casella [Ann. Statist. 8 (1980) 1036–1056, J. Amer. Statist. Assoc. 80 (1985) 753–758] by finding adaptive minimax estimators (which are, under the normality assumption, also generalized Bayes) of β, which have greater numerical stability (i.e., smaller condition number) than the usual least squares estimator. In particular, we give a subclass of such estimators which, surprisingly, has a very simple form. We also show that under certain conditions the generalized Bayes minimax estimators in the normal case are also generalized Bayes and minimax in the general case of spherically symmetric errors.
Ann. Statist., Volume 33, Number 4 (2005), 1753-1770.
First available in Project Euclid: 5 August 2005
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62C20: Minimax procedures 62C15: Admissibility 62C10: Bayesian problems; characterization of Bayes procedures
Maruyama, Yuzo; Strawderman, William E. A new class of generalized Bayes minimax ridge regression estimators. Ann. Statist. 33 (2005), no. 4, 1753--1770. doi:10.1214/009053605000000327. https://projecteuclid.org/euclid.aos/1123250228