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Partially Adaptive Estimation of Regression Models via the Generalized T Distribution

Published online by Cambridge University Press:  18 October 2010

James B. McDonald  and
Whitney K. Newey
James B. McDonald
Affiliation:
Brigham Young University
Whitney K. Newey
Affiliation:
Princeton University
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Abstract

This paper considers M-estimators of regression parameters that make use of a generalized functional form for the disturbance distribution. The family of distributions considered is the generalized t (GT), which includes the power exponential or Box-Tiao, normal, Laplace, and t distributions as special cases. The corresponding influence function is bounded and redescending for finite “degrees of freedom.” The regression estimators considered are those that maximize the GT quasi-likelihood, as well as one-step versions. Estimators of the parameters of the GT distribution and the effect of such estimates on the asymptotic efficiency of the regression estimates are discussed. We give a minimum-distance interpretation of the choice of GT parameter estimate that minimizes the asymptotic variance of the regression parameters.

Type
Research Article
Information
Econometric Theory , Volume 4 , Issue 3 , December 1988 , pp. 428 - 457
Copyright
Copyright © Cambridge University Press 1988 

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