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Adaptive estimation of the stationary density of discrete and continuous time mixing processes

Fabienne Comte, Florence Merlevède (2002)

ESAIM: Probability and Statistics

In this paper, we study the problem of non parametric estimation of the stationary marginal density f of an α or a β -mixing process, observed either in continuous time or in discrete time. We present an unified framework allowing to deal with many different cases. We consider a collection of finite dimensional linear regular spaces. We estimate f using a projection estimator built on a data driven selected linear space among the collection. This data driven choice is performed via the minimization...

Adaptive estimation of the stationary density of discrete and continuous time mixing processes

Fabienne Comte, Florence Merlevède (2010)

ESAIM: Probability and Statistics

In this paper, we study the problem of non parametric estimation of the stationary marginal density f of an α or a β-mixing process, observed either in continuous time or in discrete time. We present an unified framework allowing to deal with many different cases. We consider a collection of finite dimensional linear regular spaces. We estimate f using a projection estimator built on a data driven selected linear space among the collection. This data driven choice is performed via the minimization...

Adaptive wavelet estimation of the diffusion coefficient under additive error measurements

M. Hoffmann, A. Munk, J. Schmidt-Hieber (2012)

Annales de l'I.H.P. Probabilités et statistiques

We study nonparametric estimation of the diffusion coefficient from discrete data, when the observations are blurred by additional noise. Such issues have been developed over the last 10 years in several application fields and in particular in high frequency financial data modelling, however mainly from a parametric and semiparametric point of view. This paper addresses the nonparametric estimation of the path of the (possibly stochastic) diffusion coefficient in a relatively general setting. By...

An interpolation problem for multivariate stationary sequences

Lutz Klotz (2000)

Kybernetika

Let 𝐗 and 𝐘 be stationarily cross-correlated multivariate stationary sequences. Assume that all values of 𝐘 and all but one values of 𝐗 are known. We determine the best linear interpolation of the unknown value on the basis of the known values and derive a formula for the interpolation error matrix. Our assertions generalize a result of Budinský [1].

Aplicación de modelos de Wiener-Levy a datos biomédicos.

Charles B. Bell, F. Ramírez, E. P. Smith (1985)

Trabajos de Estadística e Investigación Operativa

Para varios conjuntos de datos biomédicos, se quiere hacer inferencia sobre la función media de la población. La mayoría de los métodos clásicos para este tipo de inferencia han sido derivados bajo el supuesto de que los datos constituyen muestras aleatorias de una población normal. Pero en realidad, en el campo médico, pocas veces se tienen muestras aleatorias. El problema práctico principal es hallar un modelo de dependencia entre los datos que aproxime la situación real y que sea manejable desde...

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