CFDP 1976

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

Author(s): 

Publication Date: December 2014

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.

Keywords: 

Nonparametric series regression, Optimal uniform convergence rates, Weak dependence, Random matrices, Splines, Wavelets, (Nonlinear) Irregular Functionals, Sieve t statistics

JEL Classification Codes:  C12, C14, C32

See CFP: 1493