A COMPARISON BETWEEN GLOBAL AND ADAPTIVE BANDWIDTHS USING (DPI) AND (RSC) SELECTION METHODS

Abstract

Non-parametric regression is type of regression analysis in which functional form of the relationship response variable and the associated predictor variable dose not to be specified in order to fit a model to a set of data. There are many different methods for non-parametric regression. We have used the local polynomial kernel estimator with the optimal choice of the smoothing parameter(s).Choosing the optimal smoothing parameter(s), which is usually called the bandwidth(s), is considered to be one the most important issue when using the kernel-based estimator. Also, the optimal bandwidth(s) played crucial role to uncover the structure of the underlying data. In this paper, we use simulation approach to make comparisons between two different strategies for selecting the optimal bandwidth(s), namely the Direct plug-In (DPI) selection method and the Residual Square Criterion (RSC) method. Within the context of these two strategies of selecting the optimal bandwidth(s), there are two different settings of choosing the smoothing parameter: global (single bandwidth) or adaptive (variable bandwidths). Moreover, four different example-regression models have been used in order to smooth the mean regression functions. Several statistical properties have been investigated in the simulation study. Such study must be restrictive because of the many possibilities to be consider, we decide to consider the following three elements: The size of sample (n). Distribution of the error's (normal, exponential). The kind of Design (fixed and random).