Abstract

In this paper, we mainly study the asymptotic normality of wavelet estimators in the heteroscedastic regression model with φ-mixing errors. Under some suitable conditions, the asymptotic normality of the wavelet estimators of g and f in the heteroscedastic regression model with φ-mixing errors are obtained, which generalize or improve the corresponding ones for α-mixing random variables and martingale difference sequence in some sense. Also, the simulation study of the finite samples provided in this paper shows the validity of our results.

中文翻译：

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具有 φ 混合误差的异方差回归模型的统计推断

摘要

在本文中，我们主要研究了具有φ-混合误差的异方差回归模型中小波估计量的渐近正态性。在一定的条件下，得到了具有φ-混合误差的异方差回归模型中g和f的小波估计量的渐近正态性，从而在一定意义上推广或改进了α-混合随机变量和鞅差序列的相应估计量。此外，本文提供的有限样本的模拟研究表明了我们结果的有效性。