We show that spline and wavelet series regression estimators for weakly dependent regressors attain the optimal uniform (i.e. sup-norm) convergence rate (n/logn)−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/p2. 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.
Authors
![Person graphic](/sites/default/files/styles/square_desktop/public/2022-06/IFS-person-graphic.png?itok=hWCtTSrz)
Yale University
![Timothy Christensen](/sites/default/files/styles/square_desktop/public/2022-07/Timothy%20Christensen.jpg?itok=OVzNRflX)
Research Associate University College London, Cemmap
Timothy is a Research Associate at IFS and a Professor of Economics at University College London.
Journal article details
- DOI
- 10.1016/j.jeconom.2015.03.010
- Publisher
- Elsevier
- Issue
- Volume 188, Issue 2, October 2015
Suggested citation
Chen, X and Christensen, T. (2015). 'Optimal uniform convergence rates and asymptotic normality for series estimators under weak dependence and weak conditions' 188(2/2015)
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