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Wavelet-based estimation of regression function with strong mixing errors under fixed design

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  • Linyuan Li
  • Yimin Xiao

Abstract

We consider wavelet-based non linear estimators, which are constructed by using the thresholding of the empirical wavelet coefficients, for the mean regression functions with strong mixing errors and investigate their asymptotic rates of convergence. We show that these estimators achieve nearly optimal convergence rates within a logarithmic term over a large range of Besov function classes Bsp, q. The theory is illustrated with some numerical examples.A new ingredient in our development is a Bernstein-type exponential inequality, for a sequence of random variables with certain mixing structure and are not necessarily bounded or sub-Gaussian. This moderate deviation inequality may be of independent interest.

Suggested Citation

  • Linyuan Li & Yimin Xiao, 2017. "Wavelet-based estimation of regression function with strong mixing errors under fixed design," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(10), pages 4824-4842, May.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:10:p:4824-4842
    DOI: 10.1080/03610926.2015.1089288
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    Cited by:

    1. Xingcai Zhou & Guang Yang & Yu Xiang, 2022. "Quantile-Wavelet Nonparametric Estimates for Time-Varying Coefficient Models," Mathematics, MDPI, vol. 10(13), pages 1-15, July.

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