Analysis of Rank Regression Modeling in Functional Data

Functional data frequently arise in various practical applications. However, traditional methods often exhibit significant performance degradation when confronted with skewed distributions or the presence of outliers. To address these challenges, this study introduces a robust methodology based on rank regression, specifically designed for functional data analysis (FDA) under non-normal distribution conditions. The proposed approach integrates three distinct forms of basis function expansions and leverages penalized least squares estimation to enable both robust variable selection and parameter estimation. This method demonstrates marked advantages in scenarios involving outliers and skewed distributions. Simulation results indicate that the proposed approach outperforms conventional robust methods, such as median regression, in terms of mean squared error and variable selection accuracy. Furthermore, its successful application to real-world data underscores its practical utility and robustness. This study provides a novel framework for robust modeling in the context of FDA.