Simulation Study for Nonparametric Regression Model with Quartic Kernel Function

Abstract

Nonparametric regression is a method for estimating the pattern of the relationship between predictor variables and response variables when the functional form of the regression curve is unknown. One estimator applicable to nonparametric regression is the Kernel estimator. The kernel estimator has a more flexible form, and the calculations are straightforward. The performance of the Kernel estimator is significantly affected by the Kernel function and the smoothing parameter (bandwidth). The method used in this study is the Kernel estimator, applied to a simulation study using a quartic kernel for optimal bandwidth selection via generalized cross-validation (GCV). This study aims to evaluate simulation results across various combinations of sample sizes and variances and to present a prediction plot of the Quartic Kernel function based on the simulation study. The results of this study are based on the Quartic Kernel function; larger sample sizes yield smaller Mean Squared Error (MSE) and GCV values and a larger coefficient of determination. In addition to sample size, variance is also very influential. The larger the variance, the larger the MSE and GCV values, and the smaller the coefficient of determination. The results of this study are prediction plots against the simulation studies used, showing that the Quartic Kernel function is less effective at predicting simulation study results. This is also evident from the accuracy obtained across different sample sizes and data with varying levels of variance, indicating that, in simulation studies using the quartic kernel estimator, predictive performance is poorer.