Generalized partially functional linear model.

Area of Science:

• Statistics
• Biostatistics
• Econometrics

Background:

• Functional data analysis is crucial for modeling complex relationships.
• Generalized partially functional linear regression offers a flexible framework for such analyses.
• Establishing asymptotic properties ensures the reliability of statistical inference.

Purpose of the Study:

• To propose a novel generalized partially functional linear regression model.
• To establish the asymptotic properties of the estimated coefficients.
• To demonstrate the model's applicability through real-world examples.

Main Methods:

• Development of a generalized partially functional linear regression model.
• Theoretical establishment of asymptotic properties for estimated coefficients.
• Application of the model to sleep quality and mortality rate datasets.

Main Results:

• The proposed model's theoretical properties were rigorously established.
• Extensive simulation experiments validated the theoretical findings.
• The model effectively analyzed the impact of various factors on sleep quality and mortality rates.

Conclusions:

• The generalized partially functional linear regression model is theoretically sound and practically applicable.
• The model provides a robust tool for analyzing complex functional data.
• The findings have implications for understanding factors influencing health and societal outcomes.