Abstract
Nadaraya-Watson (NW) kernel regression estimator is a widely used and flexible nonparametric estimator of a regression function, which is often obtained by using a fixed bandwidth. Several studies showed that the adaptive kernel estimators with varying bandwidths have better performance results. In this paper, a new improvement of the NW kernel regression estimator is proposed and the bandwidth of this new improvement is obtained depending on the range of the observations. Simulated example is presented, including comparisons with three others NW estimators. The performance of the proposed new estimator is evaluated via the MSE criterion. The results of the simulation study were very promising; it shows that our modified NW estimator performs well in all cases. Key words: Nonparametric estimation, smoothing parameter, local bandwidth factor, Nadaraya-Watson kernel regression estimator, modified Nadaraya-Watson (NW) estimator.
Highlights
In many statistical problems, nonparametric regression techniques are commonly used for describing the relationship between a response variable and some covariates
The nonparametric regression techniques are weighted averages of the response variable, where the weights depend on the technique and the distance between the observations of the explanatory variable scaled by a smoothing parameter
The purpose of this paper is to propose a new modification of the NW kernel regression estimator
Summary
Nonparametric regression techniques are commonly used for describing the relationship between a response variable and some covariates. Silverman (1986) discussed the kernel density estimation exhaustively He gave details about the assumptions of the kernel weight and the properties of the estimator such as bias and variance. He proposed an adaptation for the kernel estimator by varying the bandwidth as nonparametric density estimation. Demir and Toktamiş (2010) considered the adaptive Nadaraya-Watson (ANW) kernel regression estimators as a way to estimate the regression function The results of their simulation study showed that the NW kernel estimator has a better performance when evaluating the local bandwidth factor based on the arithmetic mean instead of using the geometric mean. MISE is the average of the ISE, and ISE is a distance measured between the fitted density and the true density which is defined as (4)
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