Abstract
We investigate the heteroscedastic regression model Yni = g(xni) + σniεni, i = 1, . . . , n, where \( {\sigma}_{ni}^2 \) = f(uni), (xni, uni) are known fixed design points, g and f are unknown functions, and the errors εni are assumed to form a stationary α-mixing random variables. Under some mild conditions, we obtain the asymptotic normality for wavelet estimators of f, prove their the asymptotic normality, and establish the Berry–Esseen-type bound for wavelet estimators of g. Also, by the given conditions we study the Berry–Esseen-type bound for estimators of g; for any δ > 0, it is of order O(n−(1/30)+δ). Finally, we have conducted comprehensive simulation studies to demonstrate the validity of obtained theoretical results.
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This work was supported by the National Natural Science Foundation of China (11271189) and the Natural Science Foundation of Guangxi (2020GXNSFBA159045).
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Ding, L., Chen, P. Wavelet estimation in heteroscedastic regression models with α-mixing random errors∗. Lith Math J 61, 13–36 (2021). https://doi.org/10.1007/s10986-021-09508-x
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DOI: https://doi.org/10.1007/s10986-021-09508-x