Comparative Analysis of Parametric and Nonparametric Methods in Scalar-on-Function Regression

The increasing prevalence of high-dimensional and complex datasets underscores the need for advanced analytical techniques in functional data analysis. This study examines regression models with a functional predictor and a scalar response, comparing three estimation methods: the functional linear model, nonparametric local linear regression, and the Nadaraya-Watson kernel estimator. Through comprehensive simulations and a real-world application, we evaluate their effectiveness in estimating the true regression operator. Results reveal that the local linear estimator consistently achieves superior predictive performance and flexibility, outperforming competing methods across all scenarios.

کلیدواژه ها:

Cross-validation ، Functional linear model ، Functional linear regression ، Nadaraya-Watson ، Nonparametric regression