Linear mixed function-on-function regression models.

Area of Science:

• Statistics
• Functional Data Analysis
• Regression Modeling

Background:

• Functional data analysis requires specialized regression models.
• Existing methods may have limitations in parameter estimation and accuracy.

Purpose of the Study:

• To develop a robust linear mixed regression model for functional response and predictor variables.
• To enhance the estimation of model parameters and variance components.

Main Methods:

• A linear mixed regression model is proposed for functional data.
• Parameter estimation is performed using the Expectation-Conditional Maximization (ECME) algorithm.
• Ensuring positive definiteness of estimated variance parameters at each iteration.

Main Results:

• The developed model demonstrates superior performance in simulation studies.
• Significant improvements observed in fitting error and Mean Squared Error (MSE) of regression coefficient estimation.
• Estimated variance parameters and covariance matrices maintain positive or positive definite properties throughout iterations.

Conclusions:

• The novel linear mixed regression model offers an effective approach for functional data analysis.
• The ECME algorithm provides a stable and accurate method for parameter estimation.
• This method advances the field of functional regression with improved accuracy and reliability.