# 34277

## Автор(ов):

1

Параметры публикации

Доклад

## Название:

Multivariate Density and Derivative Gamma Kernel Estimation by Dependent Data

## ISBN/ISSN:

978-84-9844-496-4

## Наименование конференции:

• Current Topics on Risk Analysis: ICRA6 and Risk 2015 Conference (Barcelona)

## Наименование источника:

• Proceedings of the International Conference "Current Topics on Risk Analysis: ICRA6 and Risk" (Barcelona, 2015)

• Мадрид

## Издательство:

• FUNDACIÓN MAPFRE

2015

## Страницы:

499-506
Аннотация
We consider the nonparametric estimation of the multivariate probability density function and its partial derivative with a support on $[0,\infty)$ by dependent data. We use the class of gamma-kernel estimators which are asymmetric. The gamma kernels are nonnegative and change their shape depending on the position on the semi-axis. They possess good boundary properties for a wide class of densities useful in many applications like engineering, signal processing, actuarial science etc. The theoretical asymptotic properties of the multivariate density and its partial derivative estimates like biases, variances and covariances are derived. We obtain the optimal bandwidth selection for both estimates as a minimum of the mean integrated squared error (MISE) assuming dependent data with a strong mixing. Optimal rates of convergence of the MISE are found.

## Библиографическая ссылка:

Маркович Л.А. Multivariate Density and Derivative Gamma Kernel Estimation by Dependent Data / Proceedings of the International Conference "Current Topics on Risk Analysis: ICRA6 and Risk" (Barcelona, 2015). Мадрид: FUNDACIÓN MAPFRE, 2015. С. 499-506.