Multivariate kernel density estimation with a parametric support

Abstract

Abstract. We consider kernel density estimation in the multivariate case, focusing on the use of some elements of parametric estimation. We present a two-step method, based on a modification of the EM algorithm and the generalized kernel density estimator, and compare this method with a couple of well known multivariate kernel density estimation methods.

On Hybridizations of Fourth Order Kernel of the Beta Polynomial Family.

“…Table 1 shows the classical fourth order kernels of the beta polynomial kernels and their hybrid kernels with their performance using the AMISE. As generally known, one method is better than another when it produces a smaller value of the AMISE (Jarnicka, 2009). The kernel functions denoted by * ( ) are the hybrids of the fourth order kernels.…”

Some Improvements in Nonparametric Multivariate Kernel Density Estimation

“…Clearly, in practice, one does not have access to the true density function f(x) which is to be estimated (Wand andJones 1995, Wu et al 2006). Thus, a number of approaches can be taken for finding the bandwidth that will lead to better density estimation via varying the bandwidths (Wand and Jones 1995, Katkovnik 1999, Jarnicka 2009, Ogbeide et al 2016. Details studies on the Histograms which are the oldest density methods, the Scatter plots, the Orthogonal series density, the nearest neighbour method and the Projection pursuit density estimation approaches can be seen in (Tukey 1947, Cencov 1962, Friedman and Stuetzle 1982, Rudemo 1982, Scott and Thompson 1983, Silverman 1986, Wand and Jones 1995, Isenman 1991, Bowman and Azzalini 1997.…”

Untitled

“…Clearly, in practice, one does not have access to the true density function f(x) which is to be estimated (Wand andJones 1995, Wu et al 2006). Thus, a number of approaches can be taken for finding the bandwidth that will lead to better density estimation via varying the bandwidths (Wand and Jones 1995, Katkovnik 1999, Jarnicka 2009, Ogbeide et al 2016. Details studies on the Histograms which are the oldest density methods, the Scatter plots, the Orthogonal series density, the nearest neighbour method and the Projection pursuit density estimation approaches can be seen in (Tukey 1947, Cencov 1962, Friedman and Stuetzle 1982, Rudemo 1982, Scott and Thompson 1983, Silverman 1986, Wand and Jones 1995, Isenman 1991, Bowman and Azzalini 1997.…”