# 31672

## Автор(ов):

2

Параметры публикации

Тезисы доклада

## Название:

Regularization Procedure of Signal Estimation in Multiplicative Model.

## ISBN/ISSN:

978-84-89315-69-3

## Наименование конференции:

• 2nd conference of international society for nonparametric statistics ISNPS 2014 Cadiz, Spain

## Наименование источника:

• Book of abstracts of the 2th Conference for nonparametric statistics (ISNPS 2014, Cadiz, Spain)

## Город:

• Кадис, Испания

## Издательство:

• Universidad Carlos III and ISNPS

2014

## Страницы:

39-40
Аннотация
At the previous ISNPS conference (Halkidiki’2012) the report was presented where the problem of filtering of signal with an unknown distribution from the mixture with a noise had been solved by using nonparametric kernel techniques [1]. In this paper a nonlinear multiplicative observation model with non-gaussian signal and noise is considered. The main feature of the problem is that the support of the distributions included in the evaluation functional is a positive semi-axis. Therefore, the classical methods of nonparametric estimation with symmetric kernels are not applicable because of great estimate bias. We have to apply asymmetric kernel functions of the gamma-kernel type [2]. Therefore, we have to prove the convergence theorem of nonparametric estimates of the partial density derivative entering in the equation of the optimal filtering. Moreover, we build a data-driven bandwidth for the gamma-kernel and its derivative by dependent observations. To have a stable estimates we use a regularization procedure where data-driven optimal regularization parameter is sought. Such approach leads to automatic algorithms of non-parametric filtration in multiplicative observation models. Such filtering algorithms can be used, for example, in problems of volatility estimation in models of financial mathematics.

## Библиографическая ссылка:

Добровидов А.В., Маркович Л.А. Regularization Procedure of Signal Estimation in Multiplicative Model. / Book of abstracts of the 2th Conference for nonparametric statistics (ISNPS 2014, Cadiz, Spain). Кадис, Испания: Universidad Carlos III and ISNPS, 2014. С. 39-40.