An Improved Method of Kernel Smoothing with Boundary Corrections in Nonparametric Regression Analysis

Abstract

Besides the classical parametric regression methods, the nonparametric regression is a widely used alternative method of which any predefined functions of finite number of parameters are not required. In nonparametric regression, the well known kernel smoothing techniques are of practical significance in variety of fields such as, image processing, video reconstruction, weather forecasting, modelling stock market data etc. due to their flexibility in fitting curves. However, an inherent drawback of nonparametric kernel smoothing techniques in regression is the inconsistency of the boundaries of the estimated curves, which is known as the boundary effects. Several methods have been developed to minimize such effects in density estimations, such as reflection method, boundary kernel, transformation method etc. However, the investigations for boundary corrections in nonparametric kernel smoothing in regression analysis are rare in the literature. This paper introduced a new method introducing a boundary kernel function to avoid the boundary effect of the non-parametric kernel smoothing in fitting regression curve. In this consideration, the result appeared in the series of publications for boundary correction in kernel density estimation is taken in to account for the construction of new method as an analogous extension. In this investigation, we restrict ourselves the data sets to equidistance deterministic designs (i.e. equally spaced response variable data) together with Nadaraja-Watson Smoothing Kernel Estimations. To observe the improvement of the novel approach, the simulations are presented with particularly chosen static data as a test example. In the simulations, classical parametric regression curve, regular kernel regression and the new boundary kernel estimator are employed separately for same data to compare and to examine the validity and versatility of the new boundary kernel smoothing approach. Finally, a number of graphical illustrations are used to produce some concluding remarks.