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

Authors

Shelan Saied Ismaeel, Department of Mathematics, Faculty of Science, University of Zakho, Zakho, Iraq.Follow
Kurdistan M.Taher Omar, Department of Mathematics, Faculty of Science, University of Zakho, Zakho, Iraq.Follow
Bo Wang, Department of Mathematics, University of Leicester, Leicester LE1 7RH, UKFollow

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.

Keywords

Functional data analysis, K-Nearest Neighbour stimator, Multivariate response, Nonparametric regression, Principal Component Analysis

Article Type

Supplemental Issue

How to Cite this Article

Ismaeel, Shelan Saied; Omar, Kurdistan M.Taher; and Wang, Bo (2022) "K-Nearest Neighbor Method with Principal Component Analysis for Functional Nonparametric Regression," Baghdad Science Journal: Vol. 19: Iss. 6, Article 15.
DOI: https://doi.org/10.21123/bsj.2022.6476