This paper is concerned with the estimating problem of heteroscedastic semiparametric regression model. We investigate the asymptotic normality for wavelet estimators of the slope parameter and the nonparametric component in the case of known error variance with ϕ-mixing random errors. Also, when the error variance is unknown, the asymptotic normality for the estimators of the slope parameter and the nonparametric component as well as variance function is considered under independent assumptions. Finally, the simulation study is provided to illustrate the feasibility of the theoretical result that we established.

中文翻译：

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具有随机误差的异方差半参数回归模型的统计估计

本文研究的是异方差半参数回归模型的估计问题。我们研究了在已知误差方差与 ϕ 混合随机误差的情况下斜率参数和非参数分量的小波估计量的渐近正态性。此外，当误差方差未知时，斜率参数和非参数分量以及方差函数的估计量的渐近正态性在独立假设下被考虑。最后，通过仿真研究来说明我们所建立的理论结果的可行性。