Advances and Applications in Statistics
Volume 1, Issue 1, Pages 59 - 87
(April 2001)
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ROBUST ESTIMATION OF REGRESSION AND SCALE PARAMETERS IN LINEAR MODELS
Ömer ÖztürK (USA)
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Abstract: Simultaneous robust estimates of regression and scale
parameters in a multiple linear regression model are derived from minimizing a
minimum distance criterion function. The distance function compares the p-th
power of the right and left tail probabilities of a possibly misspecified target
model. The quantity p plays the
similar role to a tuning constant in the theory of M-estimation.
The gradient of the criterion function defines M-estimating
equations. We show that the estimators are uniquely defined, asymptotically
multivariate normal with almost full efficiency. The regression and scale
estimators are as efficient as maximum likelihood estimator at the normal model.
The robustness in factor space is achieved by introducing an optimal weight
function that minimizes the trace of the asymptotic covariance matrix of the
estimator. |
Keywords and phrases: Cramer-von Mises distance, robustness, breakdown point, efficiency, optimal weights, weighted regression. |
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