Mean Consistency of Estimators in a Partially Linear Model with AANA Errors

Area of Science:

• Statistics
• Econometrics
• Data Science

Background:

• Partially linear regression models are widely used in statistical analysis.
• Understanding the properties of estimators under dependent error structures is crucial.
• Asymptotically almost negatively associated (AANA) errors present a complex dependency pattern.

Purpose of the Study:

• To investigate the statistical properties of estimators in a heteroscedastic partially linear regression model.
• To establish the p-th mean consistency of least squares and weighted least squares estimators.
• To analyze the moment convergence rates of these estimators under AANA errors.

Main Methods:

• Asymptotic analysis of estimators.
• Derivation of consistency and convergence rates.
• Simulation studies for numerical validation.

Main Results:

• The p-th mean consistency of least squares and weighted least squares estimators for both parametric and non-parametric components is established.
• The moment convergence rates of the estimators are determined.
• The results extend and improve upon existing literature for negatively associated (NA) and independent random errors.

Conclusions:

• The established theoretical results provide a robust framework for analyzing partially linear models with AANA errors.
• The findings offer improved estimation techniques and performance guarantees.
• Numerical simulations confirm the theoretical predictions and demonstrate the practical utility of the proposed methods.