On function-on-function linear quantile regression

Area of Science:

• Statistics
• Econometrics
• Functional Data Analysis

Background:

• Functional data analysis (FDA) involves data where observations are functions.
• Function-on-function regression models relationships between functions.
• Quantile regression provides a more comprehensive analysis than mean regression by estimating conditional quantiles.

Purpose of the Study:

• To introduce two novel algorithms for functional partial quantile regression.
• To accurately and efficiently estimate the regression coefficient function in function-on-function linear quantile regression models.
• To address the challenge of infinite-dimensional data in functional regression.

Main Methods:

• Functional partial quantile regression decomposition to reduce dimensionality.
• Basis expansion for approximating partial quantile regression components.
• Approximation of infinite-dimensional models using multivariate quantile regression.

Main Results:

• The proposed algorithms demonstrate superior performance in finite-sample scenarios.
• Empirical results show improved accuracy and efficiency compared to existing methods.
• Successful implementation in the R package ffpqr.

Conclusions:

• The developed algorithms provide an effective approach for functional partial quantile regression.
• These methods offer a valuable tool for analyzing complex functional data.
• The ffpqr package facilitates the application of these advanced statistical techniques.