Semiparametric Efficient Estimation of the Mean of a Time Series in the Presence of Conditional Heterogeneity of Unknown Form
研究了在创新项为平稳遍历条件对称鞅差但分布未知时，时间序列位置参数的半参数有效界，并提出了达到该界的迭代估计量和半自适应估计量。
Abstract We obtain semiparametric efficiency bounds for estimation of a location parameter in a time series model where the innovations are stationary and ergodic conditionally symmetric martingale differences but otherwise possess general dependence and distributions of unknown form. We then describe an iterative estimator that achieves this bound when the conditional density functions of the sample are known. Finally, we develop a “semi-adaptive” estimator that achieves the bound when these densities are unknown by the investigator. This estimator employs nonparametric kernel estimates of the densities. Monte Carlo results are reported.