Quadratic inference with dense functional responses

Area of Science:

• Statistics
• Functional Data Analysis

Background:

• Constant linear effect models with dense functional responses present estimation challenges.
• Existing methods may require specific correlation structure assumptions.

Purpose of the Study:

• To develop an alternative estimation method for constant linear effect models with dense functional responses.
• To leverage the quadratic inference approach for robust coefficient estimation.

Main Methods:

• Utilizing the quadratic inference approach for regression coefficient estimation.
• Employing non-parametrically estimated basis functions to avoid specifying correlation structures.
• Analyzing correlated functional data.

Main Results:

• Achieving a parametric sqrt(n)-convergence rate under specific bandwidth and data conditions.
• Establishing the asymptotic normality of the proposed estimator.
• Demonstrating superior performance compared to existing methods via simulations.

Conclusions:

• The proposed quadratic inference method provides an effective and robust solution for functional response models.
• The method achieves desirable convergence rates and asymptotic properties.
• Validated through simulations and real data analysis, showing practical utility.