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.
