Generalized Cross Validation (GCV) in Smoothing Spline Nonparametric Regression Models

Abstract

A nonparametric regression model is utilized if the the regression curve does not contain information about the accepted shape and accepted curve is exist in a function. If any curve is given without the limitation of a certain functional form, a rough and non-unique curve will result. The smoothing spline can be utilized to remove rough curves in some segments by following a curve pattern. An approach that combines nonparametric regression and smoothing spline is known as the smoothing spline nonparametric regression model. The problem in estimating is the selection and determination of smoothing parameters obtained by taking into the sum of knots used and the position of the knots so that the Generalized Cross-Validation (GCV) method is required. A study was conducted on the smoothing spline nonparametric regression model on GCV. The method used in research is a literature study obtained from some articles, journals, and books that support research achievement. The results showed that with the GCV method the minimum GCV value was obtained which would determine how well the smoothing parameters shown by the estimator did not change significantly even though the number and position of the knots varied.