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


    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
    Issue number2
    StatePublished - Oct 1 2015



    • 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