Asymptotic Normality for Wavelet Estimators in Heteroscedastic Semiparametric Model with Random Errors

DING Liwang · CHEN Ping · ZHANG Qiang · LI Yongming

Journal of Systems Science & Complexity ›› 2020, Vol. 33 ›› Issue (4) : 1212-1243.

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Journal of Systems Science & Complexity ›› 2020, Vol. 33 ›› Issue (4) : 1212-1243. DOI: 10.1007/s11424-020-8210-4

Asymptotic Normality for Wavelet Estimators in Heteroscedastic Semiparametric Model with Random Errors

  • DING Liwang · CHEN Ping · ZHANG Qiang · LI Yongming
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Abstract

For the heteroscedastic regression model Yi = xiβ + g(ti) + σiei, 1 ≤ i ≤ n, where σ2 i = f(ui), the design points (xi, ti, ui) are known and nonrandom, g(·) and f(·) are defined on the closed interval [0, 1]. When f(·) is known, we investigate the asymptotic normality for wavelet estimators of β and g(·) under {ei, 1 ≤ i ≤ n} is a sequence of identically distributed α-mixing errors; when f(·) is unknown, the asymptotic normality for wavelet estimators of β, g(·) and f(·) are established under independent errors. A simulation study is provided to illustrate the feasibility of the theoretical result that the authors derived.

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DING Liwang · CHEN Ping · ZHANG Qiang · LI Yongming. Asymptotic Normality for Wavelet Estimators in Heteroscedastic Semiparametric Model with Random Errors. Journal of Systems Science and Complexity, 2020, 33(4): 1212-1243 https://doi.org/10.1007/s11424-020-8210-4
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