Inference and diagnostics for heteroscedastic nonlinear regression models under skew scale mixtures of normal...

Area of Science:

• Statistics
• Statistical Modeling
• Data Analysis

Background:

• The heteroscedastic nonlinear regression model (HNLM) is a key tool in data modeling.
• Existing models may struggle with asymmetric and heavy-tailed data.

Purpose of the Study:

• To propose a novel HNLM incorporating skew scale mixtures of normal (SSMN) distributions.
• To enable simultaneous fitting of asymmetric and heavy-tailed data.
• To provide robust methods for estimation and diagnostics.

Main Methods:

• Maximum likelihood (ML) estimation using the expectation-maximization (EM) algorithm.
• Analytical derivation of the observed information matrix for standard error calculation.
• Diagnostic analysis employing case-deletion measures and local influence.

Main Results:

• The proposed HNLM with SSMN distributions effectively models asymmetric and heavy-tailed data.
• Simulation studies confirmed the empirical distribution of the likelihood ratio statistic and power of variance homogeneity tests.
• The method demonstrated robustness against misspecification of the structure function.

Conclusions:

• The novel HNLM offers a flexible and powerful approach for complex data.
• The developed estimation and diagnostic techniques provide reliable tools for practical applications.
• The method's utility is validated through simulation and real-data analysis.