A new class of generalized Bayes minimax ridge regression estimators

By Yuzo Maruyama, William E. Strawderman. 2004

63 citations recorded by the source corpus.

Let y = Aβ + e, where y is an N x 1 vector of observations, β is a p x 1 vector of unknown regression coefficients, A is an N x p design matrix and e is a spherically symmetric error term with unknown scale parameter a. 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.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/fc2816005e9b721216defc440cc8ea1b3fe7ea74

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Statistics and Probability

Citations in the corpus

Diagnosing and correcting the effects of multicollinearity: Bayesian implications of ridge regression (2019, background): “See for example Khalaf and Shukur 166 (2005), Lawless and Wang (1976), Nomura (1988) and Maruyama and Strawderman (2005).”