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A difference-based approach in the partially linear model with dependent errors.

Zhen Zeng1, Xiangdong Liu1

  • 1Department of Statistics, Jinan University, Guangzhou, P.R. China.

Journal of Inequalities and Applications
|October 27, 2018
PubMed
Summary
This summary is machine-generated.

This study introduces new estimators for partially linear models with dependent errors. The proposed methods achieve asymptotic normality and convergence rates, validated through simulations.

Keywords:
Asymptotic normalityFinite differenceLeast squareNSD random variablesPartially linear model

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Area of Science:

  • Statistics
  • Econometrics
  • Time Series Analysis

Background:

  • Partially linear models are widely used in statistical modeling.
  • Dependent errors in these models pose challenges for traditional estimation methods.
  • Asymptotic properties of estimators are crucial for statistical inference.

Purpose of the Study:

  • To develop and analyze estimators for both parametric and nonparametric components in partially linear models with dependent errors.
  • To establish the asymptotic normality and convergence rates of these estimators.

Main Methods:

  • Difference-based and Ordinary Least Squares (DOLS) method for the parametric component.
  • Wavelet method for the nonparametric component.
  • Asymptotic analysis to derive statistical properties.
  • Simulation studies to evaluate performance.

Main Results:

  • The DOLS estimator for the parametric component is derived and its asymptotic normality is established.
  • The wavelet estimator for the nonparametric component is obtained, with its asymptotic normality and weak convergence rate discussed.
  • Simulation results demonstrate the effectiveness of the proposed estimators.

Conclusions:

  • The study provides statistically sound estimators for partially linear models with dependent errors.
  • The proposed methods offer reliable tools for analyzing complex data structures.
  • The findings contribute to the theoretical understanding of estimation in dependent error models.