Semiparametric function-on-function quantile regression model with dynamic single-index interactions

Area of Science:

• Statistics
• Econometrics
• Biostatistics

Background:

• Longitudinal data analysis requires models that can capture complex interactions.
• Existing quantile regression models for longitudinal data often lack flexibility in modeling time-dynamic effects.

Purpose of the Study:

• To propose a novel semiparametric function-on-function quantile regression model.
• To incorporate time-dynamic single-index interactions for multivariate longitudinal/functional covariates.
• To provide a flexible framework that encompasses existing models as special cases.

Main Methods:

• Approximation of bivariate nonparametric coefficient functions using tensor product B-splines.
• Estimation of coefficient functions and index parameters via check loss minimization.
• Establishment of asymptotic normality for estimated single-index coefficients and convergence rates for coefficient functions.

Main Results:

• The proposed model effectively captures nonlinear time-dynamic interaction effects.
• Asymptotic properties of the estimators are theoretically established.
• A score test is developed to detect interaction effects.

Conclusions:

• The new semiparametric model offers a flexible and powerful tool for longitudinal data analysis.
• The method provides robust estimation and theoretical guarantees for interaction effects.
• Demonstrated utility through simulations and real-world data analysis.