Varying-Coefficient Additive Models with Density Responses and Functional Auto-Regressive Error Process

Area of Science:

• Statistics
• Data Science
• Time Series Analysis

Background:

• Autocorrelation in time-series data can lead to biased statistical inferences.
• Existing models may not adequately capture serial dependence in density-valued responses.

Purpose of the Study:

• To propose a novel varying-coefficient additive model for density-valued responses.
• To incorporate a functional auto-regressive (FAR) error process to address serial dependence.
• To provide a robust estimation procedure for analyzing serially dependent data.

Main Methods:

• Log-quantile density transformation to map density functions into a linear space.
• B-spline series approximation for initial estimation of varying-coefficient functions.
• Spline smoothing techniques to estimate the functional auto-regressive error process.
• Refinement of additive components by adjusting for the estimated error process.

Main Results:

• The proposed method effectively accounts for autocorrelation in density-valued responses.
• Theoretical properties, including convergence rates and asymptotic behavior, are established.
• Simulation studies and real-world data applications demonstrate the method's effectiveness.

Conclusions:

• The developed varying-coefficient additive model with a functional auto-regressive error process offers improved statistical inference for time-series data.
• This approach provides a valuable tool for analyzing complex, serially dependent density-valued data in various practical applications.