Optimal Uniform Convergence Rates and Asymptotic Normality for Series Estimators Under Weak Dependence and Weak Conditions

Abstract

We show that spline and wavelet series regression estimators for weakly dependent regressors attain the optimal uniform (i.e., sup-norm) convergence rate (n/log n)^{-p/(2p d)} of Stone (1982), where d is the number of regressors and p is the smoothness of the regression function. The optimal rate is achieved even for heavy-tailed martingale difference errors with finite (2 (d/p))th absolute moment for d/p