Partially Adaptive Estimation of Regression Models via the Generalized T Distribution
研究利用广义t分布作为扰动项分布的M估计量，该分布包含正态、拉普拉斯等常见分布，其影响函数有界且再下降，并讨论了分布参数估计对回归估计渐近效率的影响。
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.