This work deals with a class of discrete-time zero-sum Markov games whose state process $\left\{x_t\right\}$ evolves according to the equation $x_{t+1}=F(x_t,a_t,b_t,{\xi }_t),$ where $a_t$ and $b_t$ represent the actions of player 1 and 2, respectively, and $\left\{{\xi }_t\right\}$ is a sequence of independent and identically distributed random variables with unknown distribution $\theta$. Assuming possibly unbounded payoff, and using the empirical distribution to estimate $\theta$, we introduce approximation schemes for the value of the game as well as for optimal strategies considering both,...

Se definen en este trabajo r-desarrollos de Neumann y se prueba que toda densidad de probabilidad f admite un desarrollo r-convergente a f.Los resultados obtenidos se aplican a la estimación de f sin la suposición de que sea de cuadrado integrable, estudiándose propiedades asintóticas de los estimadores e ilustrándose con un ejemplo de aplicación.

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.

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...

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...

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 $g\circ u$. 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...

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.

Statistical inference procedures based on least absolute deviations involve estimates of a matrix which plays the role of a multivariate nuisance parameter. To estimate this matrix, we use kernel smoothing. We show consistency and obtain bounds on the rate of convergence.

We consider the problem of estimating the density $\Pi$ 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 $\Pi$ of interest.

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 $x_0\in ℝ$, over the density functions that belong to the Sobolev class $W_n(\beta ,L)$. We consider the adaptive problem setup, where the regularity parameter $\beta$ 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.

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 $x_0\in ℝ$, 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.