Statistics Papers

Document Type

Journal Article

Date of this Version

1997

Publication Source

The Annals of Statistics

Volume

25

Issue

6

Start Page

2607

Last Page

2625

DOI

10.1214/aos/1030741087

Abstract

Fixed parameter asymptotic statements are often used in the context of nonparametric curve estimation problems (e.g., nonparametric density or regression estimation). In this context several forms of superefficiency can occur. In contrast to what can happen in regular parametric problems, here every parameter point (e.g., unknown density or regression function) can be a point of superefficiency.

We begin with an example which shows how fixed parameter asymptotic statements have often appeared in the study of adaptive kernel estimators, and how superefficiency can occur in this context. We then carry out a more systematic study of such fixed parameter statements. It is shown in four general settings how the degree of superefficiency attainable depends on the structural assumptions in each case.

Keywords

superefficiency, nonparametric function estimation, asymptotics

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Date Posted: 27 November 2017

This document has been peer reviewed.