CFDP 1976

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


Publication Date: December 2014

Pages: 54


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.


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