Heteroscedastic partially linear model under skew-normal distribution with application in ragweed pollen...

Area of Science:

• Statistics
• Statistical Modeling
• Econometrics

Background:

• Traditional partially linear models (PLM) often assume constant variance (homoscedasticity), which may not hold in real-world data.
• Heteroscedasticity, where variance is not constant, can lead to biased estimates and inaccurate inferences in statistical modeling.
• The skew-normal distribution offers flexibility in modeling asymmetric data, which is common in various scientific fields.

Purpose of the Study:

• To introduce a new class of heteroscedastic partially linear models (PLM) incorporating the skew-normal distribution.
• To develop and investigate methods for parameter estimation and influence diagnostics for the proposed model.
• To present a Likelihood Ratio test for assessing scale parameter homogeneity and evaluate its performance through simulations.

Main Methods:

• Maximum likelihood estimation using the Expectation/Conditional Maximization (ECM) algorithm.
• Development of influence diagnostics tailored for the heteroscedastic PLM with skew-normal distribution.
• Likelihood Ratio test for scale parameter homogeneity and simulation studies to assess performance.

Main Results:

• The proposed heteroscedastic PLM with skew-normal distribution provides a better fit to real data (ragweed pollen concentration) than the classic homoscedastic PLM.
• Simulation studies demonstrate the effectiveness of the ECM algorithm for parameter estimation and the Likelihood Ratio test for homogeneity of variance.
• The study also considers the impact of misspecification of the structure function.

Conclusions:

• The new heteroscedastic partially linear model with skew-normal distribution is a valuable extension for analyzing data with non-constant variance and asymmetry.
• The developed estimation and testing procedures are effective and suitable for practical applications.
• This flexible modeling approach has the potential for broad applications across various scientific disciplines.