Unconditional pseudo-maximum likelihood and adaptive estimation in the presence of conditional heterogeneity of unknown form
研究了在误差项序列不相关但非独立时，使用无条件密度进行极大似然估计的后果，发现仅当回归变量严格外生时，估计量的渐近协方差矩阵才与误差独立同分布情形相同，并探讨了自适应估计的性质。
We consider parametric non-linear regression models with additive innovations which are serially uncorrelated but not necessarily independent, and consider the consequences of maximum likelihood and related one-step iterative estimation when the innovations are treated as being iid from their unconditional density. We find that the estimators' asymptotic covariance matrices will generally differ from those that would obtain if the errors actually were iid, except for the special case of strictly exogenous regressors. One important application of these results is to analysis of the properties of adaptive estimators, which employ nonparametric kernel estimates of the unconditional density of the disturbances in the construction of one-step iterative estimators. In the presence of strictly exogenous regressors, adaptive estimators are found to be asymptotically equivalent to the one-step iterative estimators that use the correct unconditional density. We illustrate our results through a brief Monte Carlo study.