On adaptive estimation in nonlinear regression
On consistency of kernel density estimators for randomly censored data : rates holding uniformly over adaptive intervals
On construction of confidence intervals for a mean of dependent data
In the report, the performance of several methods of constructing confidence intervals for a mean of stationary sequence is investigated using extensive simulation study. The studied approaches are sample reuse block methods which do not resort to bootstrap. It turns out that the performance of some known methods strongly depends on a model under consideration and on whether a two-sided or one-sided interval is used. Among the methods studied, the block method based on weak convergence result by...
On estimation of intrinsic volume densities of stationary random closed sets via parallel sets in the plane
A method of estimation of intrinsic volume densities for stationary random closed sets in based on estimating volumes of tiny collars has been introduced in T. Mrkvička and J. Rataj, On estimation of intrinsic volume densities of stationary random closed sets, Stoch. Proc. Appl. 118 (2008), 2, 213-231. In this note, a stronger asymptotic consistency is proved in dimension 2. The implementation of the method is discussed in detail. An important step is the determination of dilation radii in the...
On Fourier coefficient estimators consistent in the mean-square sense
The properties of two recursive estimators of the Fourier coefficients of a regression function with respect to a complete orthonormal system of bounded functions (ek) , k=1,2,..., are considered in the case of the observation model , i=1,...,n , where are independent random variables with zero mean and finite variance, , i=1,...,n, form a random sample from a distribution with density ϱ =1/(b-a) (uniform distribution) and are independent of the errors , i=1,...,n . Unbiasedness and mean-square...
On invariant density estimation for ergodic diffusion processes.
We present a review of several results concerning invariant density estimation by observations of ergodic diffusion process and some related problems. In every problem we propose a lower minimax bound on the risks of all estimators and then we construct an asymptotically efficient estimator.
On least squares estimation of Fourier coefficients and of the regression function
On some two-step density estimation method.
On the choice of the spline density estimators.
On the Recursive Estimation of the Location and of the Size of the Mode of a Probability Density
2000 Mathematics Subject Classification: 62G07, 62L20.Tsybakov [31] introduced the method of stochastic approximation to construct a recursive estimator of the location q of the mode of a probability density. The aim of this paper is to provide a companion algorithm to Tsybakov's algorithm, which allows to simultaneously recursively approximate the size m of the mode. We provide a precise study of the joint weak convergence rate of both estimators. Moreover, we introduce the averaging principle...
On the Strong Uniform Consistency of a New Kernel Density Estimator.
Optimal model selection in density estimation
In order to calibrate a penalization procedure for model selection, the statistician has to choose a shape for the penalty and a leading constant. In this paper, we study, for the marginal density estimation problem, the resampling penalties as general estimators of the shape of an ideal penalty. We prove that the selected estimator satisfies sharp oracle inequalities without remainder terms under a few assumptions on the marginal density and the collection of models. We also study the slope heuristic,...
Oracle inequalities and nonparametric function estimation.
Ordenes de convergencia para las aproximaciones normal y bootstrap en estimación no paramétrica de la función de densidad.
Este artículos concierne las distribuciones usadas para construir intervalos de confianza para la función de densidad en una situación no paramétrica. Se comparan los órdenes de convergencia para el límite normal, su aproximación "plug in" y el método bootstrap. Se deduce que el bootstrap se comporta mejor que las otras dos aproximaciones tanto en su forma clásica como con la aproximación bootstrap normal.