Berry-Esseen bounds for wavelet estimator in semiparametric regression model with linear process errors

Abstract

Consider the semiparametric regression model

Statistical Inference for Estimators in a Semiparametric EV Model with Linear Process Errors and Missing Responses

“…We verify that n − 1 A kn � o(n − 1/6 )a.s. for k � 4, 5, 6, 10, 11, 13. Meanwhile, from (A0)-(A3), Lemma 3,(21), and (22), one can achieve that…”

“…Many authors have been interested in the models with MA errors. For example, Liang and Jing [19] discussed asymptotic normality of estimators in partial linear models based on dependent errors; Liang and Fan [20] studied the Berry-Esseen boundary of estimators in semiparametric regression models; Wei and Li [21] established the Berry-Esseen-type bounds of wavelet estimators for β and g(•) in the semiparametric regression model with linear process errors. Zhang and Liu [22] studied the asymptotic properties for all the estimators in the semiparametric EV model with an error of negatively associated (NA) sequence under incomplete data.…”

Asymptotic properties of wavelet estimators in heteroscedastic semiparametric model based on negatively associated innovations

“…Under the mixing assumption, the asymptotic normality of the estimators for β and g were derived in [6][7][8][9]. When σ 2 i = f (u i ), model (1.1) becomes the heteroscedastic semiparametric model, Back and Liang [10], Zhang and Liang [11], and Wei and Li [12] es-tablished the strong consistency and the asymptotic normality, respectively, for the leastsquares estimators (LSEs) and weighted least-squares estimators (WLSEs) of β, based on nonparametric estimators of f and g. If g(t) ≡ 0 and σ 2 i = f (u i ), model (1.1) is reduced to the heteroscedastic linear model; when β ≡ 0 and σ 2 i = f (u i ), model (1.1) boils down to the heteroscedastic nonparametric regression model, whose asymptotic properties of unknown quantities were studied by Robinson [13], Carroll and Härdle [14], and Liang and Qi [15].…”