Details

Autor(en) / Beteiligte

• Millar, P. W.

Titel

Optimal Estimation of a General Regression Function

Ist Teil von

• The Annals of statistics, 1982-09, Vol.10 (3), p.717-740

Ort / Verlag

Institute of Mathematical Statistics

Erscheinungsjahr

1982

Link zum Volltext

Quelle

Free E-Journal (出版社公開部分のみ）

Beschreibungen/Notizen

• Let Θ be a convex subset of Rd, and for each θ ∈ Θ let F(θ; dt) be a probability on the line. For any vector an= (an1, an2, ⋯, ann) where ani∈ Θ, let Xn1, ⋯, Xnnbe independent observations, the distribution of Xnibeing F(ani; dt). The main results give a method of estimating the unknown regression function anbased on a minimum distance recipe. Under regularity assumptions, the proposed estimators are shown, in an appropriate framework, to be asymptotically normal, locally asymptotically minimax, and robust. The abstract results are illustrated by application to the linear model and to exponential response models. In general, nothing at all is assumed about the form of the regression function; accordingly, this forces the limiting normal distributions of the proposed estimators to be located on infinite dimensional linear spaces.