Improved Estimators in Nonparametric Regression Problems
作者:
LindaH. Zhao,
期刊:
Journal of the American Statistical Association
(Taylor Available online 1999)
卷期:
Volume 94,
issue 445
页码: 164-173
ISSN:0162-1459
年代: 1999
DOI:10.1080/01621459.1999.10473833
出版商: Taylor & Francis Group
关键词: Admissibility;Kernel estimators;Nonparametric regression
数据来源: Taylor
摘要:
Linear estimators of multivariate means are considered. Generalizations of some well-known theorems about admissibility of linear estimators are given. The results then are applied to show that commonly used kernel-type estimators in nonparametric regression problems can be constructively improved in a simple way. An asymptotic result is described that gives a quantitative measure of the maximum improvement to be gained in certain situations. A theoretical bound shows that gains are achievable in the relative risk of up to 58.6% (rectangular kernel) or 29.2% (Epanechnikov kernel). Some examples of smaller sample size are also investigated, and these show relative risk gains ranging up to 18% in realistic settings.
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