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

Xiaohong Chen, Timothy Christensen

    Research output: Contribution to journalArticle

    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.

    Original languageEnglish (US)
    Pages (from-to)447-465
    Number of pages19
    JournalJournal of Econometrics
    Volume188
    Issue number2
    DOIs
    StatePublished - Oct 1 2015

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    Weak Dependence
    Uniform convergence
    Asymptotic Normality
    Convergence Rate
    Exponential Inequality
    Martingale Difference
    Estimator
    Optimal Rates
    Series
    Dependent
    Regression Estimator
    Regression Function
    Random Matrices
    Splines
    Spline
    Irregular
    Smoothness
    Wavelets
    Statistics
    Moment

    Keywords

    • Nonparametric series regression
    • Optimal uniform convergence rates
    • Random matrices
    • Sieve t statistics
    • Splines
    • Wavelets (Nonlinear) Irregular functionals
    • Weak dependence

    ASJC Scopus subject areas

    • Economics and Econometrics
    • Applied Mathematics
    • History and Philosophy of Science

    Cite this

    Optimal uniform convergence rates and asymptotic normality for series estimators under weak dependence and weak conditions. / Chen, Xiaohong; Christensen, Timothy.

    In: Journal of Econometrics, Vol. 188, No. 2, 01.10.2015, p. 447-465.

    Research output: Contribution to journalArticle

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