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Partially Adaptive Estimation of Regression Models via the Generalized t Distribution

James B. McDonald and Whitney K. Newey
Econometric Theory
Vol. 4, No. 3 (Dec., 1988), pp. 428-457
Stable URL: http://www.jstor.org/stable/3532334
Page Count: 30
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Partially Adaptive Estimation of Regression Models via the Generalized t Distribution
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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.

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