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Berry-Esseen bound of wavelet estimators in heteroscedastic regression model with random errors. (English) Zbl 1499.62129

Summary: For the heteroscedastic regression model \(Y_i=x_1 \beta + g(t_i) + \sigma_i e_i\), \(1 \leq i \leq n\), where \(\sigma_i^2 = f(u_i)\), \((x_i,t_i,u_i)\) are known to be nonrandom design points, \(g(\cdot)\) and \(f(\cdot)\) are defined on the closed interval \([0,1]\). When \(f(\cdot)\) is known, we investigate the Berry-Esseen type bounds for wavelet estimators of \(\beta\) and \(g(\cdot)\) under \(\{e_i\}\) are identically distributed \(\varphi \)-mixing random errors, when \(f(\cdot)\) is unknown, the Berry-Esseen type bounds for wavelet estimators of \(\beta\), \(g(\cdot)\) and \(f(\cdot)\) established under \(\{e_i\}\) are independent random errors.

MSC:

62G08 Nonparametric regression and quantile regression
60F15 Strong limit theorems
62G20 Asymptotic properties of nonparametric inference
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