Date of this Version
The Annals of Statistics
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.
superefficiency, nonparametric function estimation, asymptotics
Brown, L. D., Low, M. G., & Zhao, L. H. (1997). Superefficiency in Nonparametric Function Estimation. The Annals of Statistics, 25 (6), 2607-2625. http://dx.doi.org/10.1214/aos/1030741087
Date Posted: 27 November 2017
This document has been peer reviewed.