Abstract
In this paper, the authors investigate the Berry-Esseen bounds of weighted kernel estimator for a nonparametric regression model based on linear process errors under a LNQD random variable sequence. The rate of the normal approximation is shown as O(n^{-1/6}) under some appropriate conditions. The results obtained in the article generalize or improve the corresponding ones for mixing dependent sequences in some sense.
Highlights
1 Introduction We discuss that the estimation of the fixed design nonparametric regression model involves a regression function g(·) which is defined on a closed interval [0, 1]: Yi = g(ti) + εi (1 ≤ i ≤ n), (1.1)
Li et al [14] established the Berry-Esseen bounds of the wavelet estimator for a nonparametric regression model with linear process errors generated by φ-mixing sequences
There are very few literature works on Berry-Esseen bounds of weighted kernel estimator for nonparametric regression model (1.1) with linear process errors
Summary
Wang and Zhang [12] obtained a Berry-Esseen type estimate for NA random variables with only finite second moment They improved the convergence rate result in the central limit theorem and precise asymptotics in the law of the iterated logarithm for NA and linearly negative quadrant dependent sequences. Li et al [14] established the Berry-Esseen bounds of the wavelet estimator for a nonparametric regression model with linear process errors generated by φ-mixing sequences. There are very few literature works on Berry-Esseen bounds of weighted kernel estimator for nonparametric regression model (1.1) with linear process errors. The main purpose of the paper is to investigate the Berry-Esseen bounds of weighted kernel estimator for nonparametric regression model with linear process errors generated by a LNQD sequence.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
