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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.
Authors
Yale University
Research Associate University College London, Cemmap
Timothy is a Research Associate at IFS and a Professor of Economics at University College London.
Working Paper details
- DOI
- 10.1920/wp.cem.2014.4614
- Publisher
- IFS
Suggested citation
Chen, X and Christensen, T. (2014). Optimal uniform convergence rates and asymptotic normality for series estimators under weak dependence and weak conditions. London: IFS. Available at: https://ifs.org.uk/publications/optimal-uniform-convergence-rates-and-asymptotic-normality-series-estimators-under (accessed: 14 May 2024).
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