Nonparametric Estimation of Multivariate Density and its Derivative by Dependent Data Using Gamma Kernels

We consider the nonparametric estimation of multivariate probability density function and its partial derivative with a support on nonnegative axis by dependent data. use class kernel estimators asymmetric gamma functions. The kernels are nonnegative; they may change their shape depending position semi-axis possess good boundary properties for wide densities. Asymptotic estimates derivatives such as biases, variances, covariances derived. optimal bandwidth both is obtained minimum mean integrated squared error (MISE) data strong mixing. Optimal convergence rates MISE found.