Estimating the mean function of a Gaussian process and the Stein effect


Journal Article

The problem of global estimation of the mean function θ(·) of a quite arbitrary Gaussian process is considered. The loss function in estimating θ by a function a(·) is assumed to be of the form L(θ, a) = ∫ [θ(t) - a(t)]2μ(dt), and estimators are evaluated in terms of their risk function (expected loss). The usual minimax estimator of θ is shown to be inadmissible via the Stein phenomenon; in estimating the function θ we are trying to simultaneously estimate a larger number of normal means. Estimators improving upon the usual minimax estimator are constructed, including an estimator which allows the incorporation of prior information about θ. The analysis is carried out by using a version of the Karhunen-Loéve expansion to represent the original problem as the problem of estimating a countably infinite sequence of means from independent normal distributions. © 1983.

Full Text

Duke Authors

Cited Authors

  • Berger, J; Wolpert, R

Published Date

  • January 1, 1983

Published In

Volume / Issue

  • 13 / 3

Start / End Page

  • 401 - 424

Electronic International Standard Serial Number (EISSN)

  • 1095-7243

International Standard Serial Number (ISSN)

  • 0047-259X

Digital Object Identifier (DOI)

  • 10.1016/0047-259X(83)90018-0

Citation Source

  • Scopus