A Key Note on Performance of Smoothing Parameterizations in Kernel Density Estimation

Authors

Israel U. Siloko, Edo University Iyamho, Department of Mathematics and Computer Science, P.M.B. 04, AuchiFollow
Osayomore Ikpotokin, Ambrose Alli University, P.M.B. 14, Ekpoma, Department of Mathematics and Statistics,NigeriaFollow
Edith A. Siloko, University of Benin, Department of Mathematics, P.M.B. 1154, Benin City, NigeriaFollow

Section

Mathematics and Computational Sciences

Abstract

The univariate kernel density estimator requires one smoothing parameter while the bivariate and other higher dimensional kernel density estimatorsdemand more than one smoothing parameter depending on the form of smoothing parameterizations used. The smoothing parameters of the higher dimensional kernels are presented in a matrix form called the smoothing matrix. The two forms of parameterizations frequently used in higher dimensional kernel estimators are diagonal or constrained parameterization and full or unconstrained parameterization. While thefull parameterization has no restrictions, the diagonal hassome form of restrictions.Thestudyinvestigates the performance of smoothing parameterizations of bivariate kernel estimator using asymptotic mean integrated squared error aserror criterion function. The results show that in retention of statistical properties of data and production of smaller values of asymptotic mean integrated squared error as tabulated, the full smoothing parameterization outperforms its diagonal counterpart.

Recommended Citation

Siloko, Israel U.; Ikpotokin, Osayomore; and Siloko, Edith A. (2019) "A Key Note on Performance of Smoothing Parameterizations in Kernel Density Estimation," Tanzania Journal of Science: Vol. 45: Iss. 1, Article 1.
Available at:https://doi.org/10.65085/2507-7961.1717