Berry–Esseen bound of wavelet estimators in heteroscedastic regression model with random errors

Ding, Lei; Chen, Ping; Li, Yongming

doi:10.1080/00207160.2018.1487958

Cited by 6 publications

(2 citation statements)

References 22 publications

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“…Reference [24] considered a wavelet estimator for the mean regression function with strong mixing errors and investigated their asymptotic rates of convergence by using the thresholding of the empirical wavelet coefficients. References [25,26] showed Berry-Esseen-type bounds on wavelet estimators for semiparametric models under dependent errors. For varying coefficient models, references [27,28] provided wavelet estimation and studied convergence rate and asymptotic normality under i.i.d.…”

Section: Introductionmentioning

confidence: 99%

Quantile-Wavelet Nonparametric Estimates for Time-Varying Coefficient Models

Zhou¹,

Yang²

2022

Mathematics

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The paper considers quantile-wavelet estimation for time-varying coefficients by embedding a wavelet kernel into quantile regression. Our methodology is quite general in the sense that we do not require the unknown time-varying coefficients to be smooth curves of a common degree or the errors to be independently distributed. Quantile-wavelet estimation is robust to outliers or heavy-tailed data. The model is a dynamic time-varying model of nonlinear time series. A strong Bahadur order O2mn3/4(logn)1/2 for the estimation is obtained under mild conditions. As applications, the rate of uniform strong convergence and the asymptotic normality are derived.

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Section: Introductionmentioning

confidence: 99%

Quantile-Wavelet Nonparametric Estimates for Time-Varying Coefficient Models

Zhou¹,

Yang²

2022

Mathematics

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“…Li and Xiao [25] considered a wavelet estimator for the mean regression function with strong mixing errors and investigated their asymptotic rates of convergence by using the thresholding of the empirical wavelet coefficients. Berry-Esseen type bounds for wavelet estimators for semiparametric regression models were studied by [26,27]. For the nonparametric models (1.1), as we learned, no study on L 1 -wavelet estimators is reported.…”

Section: Introductionmentioning

confidence: 99%

Asymptotics for $L_{1}$-wavelet method for nonparametric regression

Zhou

Fang-xia

2020

J Inequal Appl

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Wavelets are particularly useful because of their natural adaptive ability to characterize data with intrinsically local properties. When the data contain outliers or come from a population with a heavy-tailed distribution, L 1-estimation should obtain a better fit. In this paper, we propose a L 1-wavelet method for nonparametric regression, and derive the asymptotic properties of the L 1-wavelet estimator, including the Bahadur representation, the rate of convergence and asymptotic normality. The rate of convergence of it is comparable with the optimal convergence rate of the nonparametric estimation in nonparametric models, and it does not require the continuously differentiable conditions of a nonparametric function.

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The adaptivity of thresholding wavelet estimators in heteroscedastic nonparametric model with negatively super-additive dependent errors

Liu

et al. 2020

J. Korean Stat. Soc.

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Berry–Esseen bound of wavelet estimators in heteroscedastic regression model with random errors

Cited by 6 publications

References 22 publications

Quantile-Wavelet Nonparametric Estimates for Time-Varying Coefficient Models

Quantile-Wavelet Nonparametric Estimates for Time-Varying Coefficient Models

Asymptotics for $L_{1}$-wavelet method for nonparametric regression

The adaptivity of thresholding wavelet estimators in heteroscedastic nonparametric model with negatively super-additive dependent errors

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