Title

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

Document Type

Discussion Paper

Publication Date

12-1-2014

CFDP Number

1976

CFDP Pages

54

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 < 2. We also establish the asymptotic normality of t statistics for possibly nonlinear, irregular functionals of the conditional mean function under weak conditions. The results are proved by deriving a new exponential inequality for sums of weakly dependent random matrices, which is of independent interest.

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