A note on adaptation in garch models
在Engle型GARCH模型中，发现一类对称和非对称密度函数能使半参数估计量的渐近效率等于极大似然估计量，并刻画了最小化参数得分与半参数得分均方距离的解，其中拉普拉斯密度表现突出。
In the framework of the Engle-type (G)ARCH models, I demonstrate that there is a family of symmetric and asymmetric density functions for which the asymptotic efficiency of the semiparametric estimator is equal to the asymptotic efficiency of the maximum likelihood estimator. This family of densities is bimodal (except for the normal). I also chracterize the solution to the problem of minimizing the mean squared distance between the parametric score and the semiparametric score in order to search for unimodal densities for which the semiparametric estimator is likely to perform well. The LaPlace density function emerges as one of these cases.