Comparative Analysis of Predictive Performance in Nonparametric Functional Regression: A Case Study of Spectrometric Fat Content Prediction

Abstract

Objective: This research aims to compare two nonparametric functional regression models, the Kernel Model and the K-Nearest Neighbor (KNN) Model, with a focus on predicting scalar responses from functional covariates. Two semi-metrics, one based on second derivatives and the other on Functional Principle Component Analysis, are employed for prediction. The study assesses the accuracy of these models by computing Mean Square Errors (MSE) and provides practical applications for illustration. Method: The study delves into the realm of nonparametric functional regression, where the response variable (Y) is scalar, and the covariate variable (x) is a function. The Kernel Model, known as funopare.kernel.cv, and the KNN Model, termed funopare.knn.gcv, are used for prediction. The Kernel Model employs automatic bandwidth selection via Cross-Validation, while the KNN Model employs a global smoothing parameter. The performance of both models is evaluated using MSE, considering two different semi-metrics. Results: The results indicate that the KNN Model outperforms the Kernel Model in terms of prediction accuracy, as supported by the computed MSE. The choice of semi-metric, whether based on second derivatives or Functional Principle Component Analysis, impacts the model's performance. Two real-world applications, Spectrometric Data for predicting fat content and Canadian Weather Station data for predicting precipitation, demonstrate the practicality and utility of the models. Conclusion: This research provides valuable insights into nonparametric functional regression methods for predicting scalar responses from functional covariates. The KNN Model, when compared to the Kernel Model, offers superior predictive performance. The selection of an appropriate semi-metric is essential for model accuracy. Future research may explore the extension of these models to cases involving multivariate responses and consider interactions between response components.