K-Nearest Neighbor Method with Principal Component Analysis for Functional Nonparametric Regression

Abstract

This paper proposed a new  method to study functional non-parametric regression data analysis with conditional expectation in the case that the covariates  are functional and the Principal Component Analysis was utilized to de-correlate the multivariate response variables. It  utilized the formula of the Nadaraya Watson estimator (K-Nearest Neighbour (KNN)) for prediction with different types of the semi-metrics, (which are based on Second Derivative and Functional Principal Component Analysis (FPCA))  for measureing the closeness between curves.  Root Mean Square Errors is used for the  implementation of this model which is then compared to the independent response method. R program is used for analysing data. Then, when  the covariates  are functional and the Principal Component Analysis was utilized to de-correlate the multivariate response variables model, results are more preferable than the independent response method. The models are demonstrated by both a simulation data and real data.