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

Xiaohong Chen () and Timothy M. Christensen
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Timothy M. Christensen: NYU

No 1976, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

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

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)
Pages: 54 pages
Date: 2014-12
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (6)

Published in Journal of Econometrics (October 2015), 188(2): 447-465

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Related works:
Journal Article: Optimal uniform convergence rates and asymptotic normality for series estimators under weak dependence and weak conditions (2015)
Working Paper: Optimal uniform convergence rates and asymptotic normality for series estimators under weak dependence and weak conditions (2014)
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