Optimal uniform convergence rates and asymptotic normality for series estimators under weak dependence and weak conditions

Xiaohong Chen () and Timothy M. Christensen

Journal of Econometrics, 2015, vol. 188, issue 2, 447-465

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/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/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 (search for similar items in EconPapers)
JEL-codes: C12 C14 C32 (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (95)

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Related works:
Working Paper: Optimal Uniform Convergence Rates and Asymptotic Normality for Series Estimators under Weak Dependence and Weak Conditions (2014)
Working Paper: Optimal uniform convergence rates and asymptotic normality for series estimators under weak dependence and weak conditions (2014)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:188:y:2015:i:2:p:447-465

DOI: 10.1016/j.jeconom.2015.03.010

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