A Discourse on Smoothing Parameterizations using Hypothetical Dataset

Abstract

The univariate kernel estimator usually requires a smoothing parameter, unlike the multi-dimensional estimators that necessarily require more smoothing parameters. The smoothing parameter(s) of kernels with a higher dimension may be called smoothing matrices. Kernels of higher dimensions have three kinds of parameterizations as estimators viz: constant, diagonal, and full parameterizations. Unlike the full parameterization, the diagonal parameterization exhibit some levels of restrictions. This study attempts to reconnoiter the coherence exhibited by kernel estimators especially where smoothing parameterizations are employed. In this discourse, asymptotic mean-integrated squared error(AMISE) is used as a criterion function and bivariate cases alone are considered. With some hypothetical data, the results show that full smoothing parameterization outperformed the constant and diagonal parameterizations in respect of the asymptotic mean-integrated squared error’s value and the kernel estimate’s ability to retain the true characteristics of the affected distribution.