Gamma kernel estimation of multivariate density and its derivative on the nonnegative semiaxis by dependent data
Abstract
In this paper, we consider the nonparametric estimation of the multivariate probability density function and its partial derivative with a support on $[0,\infty)$. To this end we use the class of kernel estimators with asymmetric gamma kernel functions. The gamma kernels are nonnegative. They change their shape depending on the position on the semiaxis and are robust to the boundary bias problem. We investigate the mean integrated squared error (MISE) assuming dependent data with strong mixing and find the optimal bandwidth of the kernel as a minimum of the MISE. We derive the bias, the variance and the covariance of the density and of its partial derivative.
 Publication:

arXiv eprints
 Pub Date:
 October 2014
 arXiv:
 arXiv:1410.2507
 Bibcode:
 2014arXiv1410.2507M
 Keywords:

 Mathematics  Probability
 EPrint:
 Version with exaples