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Fundam. Prikl. Mat., 2018, Volume 22, Issue 3, Pages 145–177 (Mi fpm1809)  

Nonparametric estimation of multivariate density and its derivative by dependent data using gamma kernels

L. A. Markovichab

a Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow
b V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow

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

Funding Agency Grant Number
Russian Science Foundation 14-50-00150


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UDC: 519.213

Citation: L. A. Markovich, “Nonparametric estimation of multivariate density and its derivative by dependent data using gamma kernels”, Fundam. Prikl. Mat., 22:3 (2018), 145–177

Citation in format AMSBIB
\Bibitem{Mar18}
\by L.~A.~Markovich
\paper Nonparametric estimation of multivariate density and its derivative by dependent data using gamma kernels
\jour Fundam. Prikl. Mat.
\yr 2018
\vol 22
\issue 3
\pages 145--177
\mathnet{http://mi.mathnet.ru/fpm1809}


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  • Фундаментальная и прикладная математика
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