Applied Mathematical Sciences, Vol. 9, 2015, no. 122, 6083 - 6094
HIKARI Ltd, www.m-hikari.com
http://dx.doi.org/10.12988/ams.2015.58517
The Combination of Spline and Kernel
Estimator for Nonparametric Regression
and its Properties
I Nyoman Budiantara, Vita Ratnasari, Madu Ratna and Ismaini Zain
Statistics Department, Sepuluh Nopember Institute of Technology
Kampus ITS, Sukolilo, Surabaya, Indonesia
Copyright © 2015 I Nyoman Budiantara, Vita Ratnasari, Madu Ratna and Ismaini Zain. This
article is distributed under the Creative Commons Attribution License, which permits unrestricted
use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Consider additive nonparametric regression model with two predictor variables
components. In the first predictor component, the regression curve is approached
using Spline regression, and in the second predictor component, the regression
curve is approached using Kernel regression. Random error of regression model is
assumed to have independent normal distribution with zero mean and the same
variance. This article provides an estimator of Spline regression curve, estimator
of Kernel regression curve, and an estimator of a combination of Spline and
Kernel regressions. The produced estimators are biased estimators, but all
estimators are classified as linear estimators in observation. Estimator of a
combination of Spline and Kernel regression depended on knot points and
bandwith parameter. The best estimator of a combination of Spline and Kernel
regression is found by minimizing Generalized Cross Validation (GCV) function.
Keywords: Nonparametric Regression, Spline, Kernel, Mixed Estimator, GCV
1. Introduction
In recent decades, nonparametric regression has received a lot of attention
from researchers. Nonparametric regression is a regression model approached
used if the pattern of relation between predictor variable and response isn’t known,
or if there is no complete past information on the shape of data pattern [1], [2], [3].
The nonparametric regression models which receive a lot of attention from re-