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

Author

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  • Xiaohong Chen

    (Institute for Fiscal Studies and Yale University)

  • Timothy M. Christensen

    (Institute for Fiscal Studies)

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

Suggested Citation

  • Xiaohong Chen & Timothy M. Christensen, 2014. "Optimal uniform convergence rates and asymptotic normality for series estimators under weak dependence and weak conditions," CeMMAP working papers CWP46/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:cemmap:46/14
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    References listed on IDEAS

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    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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