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Estimación de la función cuantil y cuantildensidad mediante polinomios de Kantorovic.

Ana Fernández Palacín, José Muñoz Pérez (1990)

Trabajos de Estadística

En este trabajo se propone un estimador para la función cuantil, basado en polinomios de Kantorovic, como estimador natural, y se prueba que su error absoluto medio es un infinitésimo de orden n-1/2. Mediante simulación se pone de manifiesto que dicho estimador conduce a una reducción sustancial del error absoluto medio frente a la función cuantil muestral y, por otra parte, se compara con el estimador basado en polinomios de Bernstein.

Estimación no paramétrica de curvas notables para datos dependientes.

Juan Manuel Vilar Fernández (1989)

Trabajos de Estadística

Sea {Xt: t ∈ Z} una serie de tiempo estacionaria, con valores en Rp, verificando la condición de ser α-mixing o L2-estable. A partir de una muestra de tamaño n se define una amplia clase de estimadores no paramétricos de la función de densidad f(x) asociada al proceso, y de la función de autorregresión de orden k:r(y) = E(g(Xt+1)/(Xt-k+1 ... Xt) = y), y ∈ Rksiendo g una función real.Se estudian las siguientes propiedades asintóticas de estos estimadores: consistencia puntual (casi segura y en media...

Estimación no paramétrica de la función de riesgo: aplicaciones a sismología.

Graciela Estévez Pérez, Alejandro Quintela del Río (2001)

Qüestiió

Se estudia la estimación de tipo no paramétrico de la función de riesgo o razón de fallo de una variable aleatoria real. A partir de una muestra X1, X2, ..., Xn de datos no censurados y no necesariamente independientes, se considera un estimador cociente entre el estimador núcleo de la función de densidad y un estimador núcleo de la función de supervivencia, sobre el que se estudia el problema de selección del parámetro ventana. Por medio de un estudio de simulación se observa la ventaja de utilizar...

Estimating composite functions by model selection

Yannick Baraud, Lucien Birgé (2014)

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

We consider the problem of estimating a function s on [ - 1 , 1 ] k for large values of k by looking for some best approximation of s by composite functions of the form g ∘ u . Our solution is based on model selection and leads to a very general approach to solve this problem with respect to many different types of functions g , u and statistical frameworks. In particular, we handle the problems of approximating s by additive functions, single and multiple index models, artificial neural networks, mixtures of Gaussian...

Estimation and tests in finite mixture models of nonparametric densities

Odile Pons (2009)

ESAIM: Probability and Statistics

The aim is to study the asymptotic behavior of estimators and tests for the components of identifiable finite mixture models of nonparametric densities with a known number of components. Conditions for identifiability of the mixture components and convergence of identifiable parameters are given. The consistency and weak convergence of the identifiable parameters and test statistics are presented for several models.

Estimation of the density of a determinantal process

Yannick Baraud (2013)

Confluentes Mathematici

We consider the problem of estimating the density Π of a determinantal process N from the observation of n independent copies of it. We use an aggregation procedure based on robust testing to build our estimator. We establish non-asymptotic risk bounds with respect to the Hellinger loss and deduce, when n goes to infinity, uniform rates of convergence over classes of densities Π of interest.

Exact adaptive pointwise estimation on Sobolev classes of densities

Cristina Butucea (2001)

ESAIM: Probability and Statistics

The subject of this paper is to estimate adaptively the common probability density of n independent, identically distributed random variables. The estimation is done at a fixed point x 0 ∈ ℝ , over the density functions that belong to the Sobolev class W n ( β , L ) . We consider the adaptive problem setup, where the regularity parameter β is unknown and varies in a given set B n . A sharp adaptive estimator is obtained, and the explicit asymptotical constant, associated to its rate of convergence is found.

Exact adaptive pointwise estimation on Sobolev classes of densities

Cristina Butucea (2010)

ESAIM: Probability and Statistics

The subject of this paper is to estimate adaptively the common probability density of n independent, identically distributed random variables. The estimation is done at a fixed point x 0 ∈ ℝ , over the density functions that belong to the Sobolev class Wn(β,L). We consider the adaptive problem setup, where the regularity parameter β is unknown and varies in a given set Bn. A sharp adaptive estimator is obtained, and the explicit asymptotical constant, associated to its rate of convergence is found.

Funcionales de mínima g-divergencia y sus estimadores asociados (II).

Francisco Javier Cano Sevilla, M.ª Pilar Lasala Calleja (1984)

Trabajos de Estadística e Investigación Operativa

Se realizan dos estudios de simulación para comprobar el comportamiento asintóticamente robusto del estimador de mínima g-divergencia para dos elecciones notables de la función g.

Funcionales de mínima g-divergencia y sus estimadores asociados (I).

Francisco José Cano Sevilla, M.ª Pilar Lasala Calleja (1984)

Trabajos de Estadística e Investigación Operativa

Se introducen los funcionales de mínima g-divergencia y sus estimadores asociados. Se prueba la existencia y robustez del funcional y la convergencia del estimador asociado.

Gaussian model selection

Lucien Birgé, Pascal Massart (2001)

Journal of the European Mathematical Society

Our purpose in this paper is to provide a general approach to model selection via penalization for Gaussian regression and to develop our point of view about this subject. The advantage and importance of model selection come from the fact that it provides a suitable approach to many different types of problems, starting from model selection per se (among a family of parametric models, which one is more suitable for the data at hand), which includes for instance variable selection in regression models,...

Generalized covariance inequalities

Przemysław Matuła, Maciej Ziemba (2011)

Open Mathematics

We prove some inequalities for the difference between a joint distribution and the product of its marginals for arbitrary absolutely continuous random variables. Some applications of the obtained inequalities are also presented.

Generalized regression estimation for continuous time processes with values in functional spaces

Bertrand Maillot, Christophe Chesneau (2021)

Commentationes Mathematicae Universitatis Carolinae

We consider two continuous time processes; the first one is valued in a semi-metric space, while the second one is real-valued. In some sense, we extend the results of F. Ferraty and P. Vieu in ``Nonparametric models for functional data, with application in regression, time-series prediction and curve discrimination'' (2004), by establishing the convergence, with rates, of the generalized regression function when a real-valued continuous time response is considered. As corollaries, we deduce the...

Kernel estimators and the Dvoretzky-Kiefer-Wolfowitz inequality

Ryszard Zieliński (2007)

Applicationes Mathematicae

It turns out that for standard kernel estimators no inequality like that of Dvoretzky-Kiefer-Wolfowitz can be constructed, and as a result it is impossible to answer the question of how many observations are needed to guarantee a prescribed level of accuracy of the estimator. A remedy is to adapt the bandwidth to the sample at hand.

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