ADAPTIVE NONPARAMETRIC REGRESSION WITH CONDITIONAL HETEROSKEDASTICITY
研究了在误差项存在条件异方差时，如何自适应地估计非参数回归模型中的条件均值和条件方差函数，提出基于局部剖面似然的一步牛顿-拉夫森估计和局部剖面似然估计，并证明其渐近等价于已知误差分布时的不可行局部似然估计。
In this paper, we study adaptive nonparametric regression estimation in the presence of conditional heteroskedastic error terms. We demonstrate that both the conditional mean and conditional variance functions in a nonparametric regression model can be estimated adaptively based on the local profile likelihood principle. Both the one-step Newton–Raphson estimator and the local profile likelihood estimator are investigated. We show that the proposed estimators are asymptotically equivalent to the infeasible local likelihood estimators [e.g., Aerts and Claeskens (1997) Journal of the American Statistical Association 92, 1536–1545], which require knowledge of the error distribution. Simulation evidence suggests that when the distribution of the error term is different from Gaussian, the adaptive estimators of both conditional mean and variance can often achieve significant efficiency over the conventional local polynomial estimators.