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

Linyuan Li and Yimin Xiao

Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 10, 4824-4842

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.

Date: 2017
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DOI: 10.1080/03610926.2015.1089288

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