Abstract

The two-dimensional kernel estimators are very important because graphical presentation of data beyond three dimensional forms is oftentimes not too frequently employed in data visualizations. The frequency of the bivariate estimator in the multivariate setting is attributed to the sparseness of data that is associated with increase in dimension. The performance of bivariate kernel is reliant on the smoothing parameter and other statistical parameters. While the smoothness of the estimates generated by the kernel estimator is primarily regulated by the smoothing parameter, its performance numerically may be depended on other statistical parameters. One of the popular performance metrics in kernel estimation is the asymptotic mean integrated squared error (AMISE) whose popularity is occasioned by its mathematical tractability and the inclusion of dimension with respect to performance evaluation. The computation of the bivariate kernel AMISE besides the smoothing parameter depends on basic statistical properties such as correlation coefficient and standard deviations of the observations. This paper compares the performance of the bivariate kernel using the correlation coefficient, standard deviations and the smoothing parameter. The results of the comparison show that for bivariate observations with independent standard deviations and correlated, the AMISE values is smaller than the AMISE values computed with the smoothing parameter.

Key Words: AMISE, Kernel, Smoothing Parameter, Standard Deviation, Correlation Coefficient