A Bounded Influence, High Breakdown, Efficient Regression Estimator
作者:
ClintW. Coakley,
ThomasP. Hettmansperger,
期刊:
Journal of the American Statistical Association
(Taylor Available online 1993)
卷期:
Volume 88,
issue 423
页码: 872-880
ISSN:0162-1459
年代: 1993
DOI:10.1080/01621459.1993.10476352
出版商: Taylor & Francis Group
关键词: Breakdown point;GeneralMestimator;Influence function;Newton-Raphson;One-step estimator;Regression
数据来源: Taylor
摘要:
We consider the multiple linear regression modelyi=x′iβ+εi,i= 1, 2, …,n, with random carriers and focus on the estimation ofβ. This article's main contribution is to present an estimator that is affine, regression, and scale equivariant; has both a high breakdown point and a bounded influence function; and has an asymptotic efficiency greater than .95 versus least squares under Gaussian errors. We give conditions under which the estimator—a one-step generalMestimator that uses Schweppe weights and is based on a high breakdown initial estimator—satisfies these properties. The major conditions necessary for the estimator are (a) it must be based on a √n-consistent initial estimator with a 50% breakdown point, and (b) it must be based on a psi function that is odd, bounded, and strictly increasing. The advantage of this estimator over previous approaches is that it does not downweight high leverage points without first considering how they fit the bulk of the data. Methods of computing diagnostics and constructing Wald-type tests about β are given. We illustrate the features of the estimator on a data set with two regressors, showing how a good leverage point is not downweighted, whereas a bad leverage point is downweighted.
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