For the heteroscedastic regression model Y_i = x_iβ + g(t_i) + σ_ie_i, 1 ≤ i ≤ n, where σ ²_i = f (u_i), the design points (x_i, t_i, u_i) 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 {e_i, 1 ≤ i ≤ n} is a sequence of identically distributed a-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.

中文翻译：

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具有随机误差的异方差半参数模型中小波估计的渐近正态性

对于异方差回归模型Ŷ_我= X_我β +克（吨_我）+ σ_我ë_我，1≤我≤ Ñ，其中σ ²_我= ˚F（Ú_我），设计点（X_我，Ť_我，u _i）是已知的，并且在封闭区间[0,1]上定义了非随机g（·）和f（·）。当f （·）是已知的，我们探讨的小波估计的渐近正态β和克下（·）{ Ë_我，1≤我≤ Ñ }是分布式的相同的序列的混合的错误; 当f（·）未知时，在独立误差下建立β，g（·）和f（·）的小波估计的渐近正态性。提供了一个仿真研究，以说明作者得出的理论结果的可行性。