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Berry-Esseen bounds of weighted kernel estimator for a nonparametric regression model based on linear process errors
Liwang Ding1,2, Ping Chen1, Yongming Li3
11School of Science, Nanjing University of Science and Technology, Nanjing, 210094 P.R. China.
Journal of Inequalities and Applications
|January 26, 2018
Summary
This study examines Berry-Esseen bounds for weighted kernel estimators in nonparametric regression with linear process errors. The research establishes the rate of normal approximation for these estimators under specific conditions.
Area of Science:
- Statistics
- Probability Theory
- Econometrics
Background:
- Nonparametric regression is crucial for modeling complex relationships.
- Kernel estimators are widely used but require understanding their approximation properties.
- Linear process errors and dependent random variables present challenges in statistical analysis.
Purpose of the Study:
- To investigate the Berry-Esseen bounds for a weighted kernel estimator.
- To analyze the estimator within a nonparametric regression model framework.
- To consider errors following a linear process under a Long-range Negative Quadrant Dependence (LNQD) sequence.
Main Methods:
- Application of Berry-Esseen theorems.
- Analysis of weighted kernel estimators.
- Derivation of normal approximation rates for dependent sequences.
Main Results:
- The paper establishes the rate of normal approximation for the weighted kernel estimator.
- The derived rate is shown to be [Formula: see text] under specific conditions.
- The findings extend existing results for various mixing dependent sequences.
Conclusions:
- The study provides theoretical guarantees for the accuracy of the weighted kernel estimator.
- The results contribute to the understanding of statistical inference for dependent data.
- The work generalizes and improves upon previous findings in nonparametric regression analysis.
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