Abstract

ESTIMATION OF EFFICIENCIES OF THE BIVARIATE DERIVATIVES OF SMOOTH POLYNOMIAL KERNELS.

Siloko, I. U.; Ikpotokin, O. and Siloko, E. A.3

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Abstract The bivariate kernel estimator bridges the gap between the univariate kernel and higher dimensional kernels in density estimation. The efficiencies of the univariate kernels have received considerable attention unlike their bivariate counterparts due to the ?curse of dimensionality? effect. In this paper, our focus is on the efficiencies of the derivatives of the bivariate kernels of the Uniform, Epanechnikov, Biweight, Triweight, Quadriweight and Gaussian kernels which are members of the beta polynomial family. The bivariate form of these kernel functions were obtain from their univariate counterpart using the product approach. The results obtain shows that the efficiency of the kernels decrease as the powers of the polynomial increases and tends to increase as the derivative order increases. Key words: Kernel Density Derivatives, Smooth Polynomial Kernels, Efficiency of Kernels, Asymptotic Mean Integrated Squared Error.

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