Adaptive maximum-likelihood-like estimation in linear models. II. Asymptotic normality
Adaptive non-asymptotic confidence balls in density estimation
We build confidence balls for the common density s of a real valued sample X1,...,Xn. We use resampling methods to estimate the projection of s onto finite dimensional linear spaces and a model selection procedure to choose an optimal approximation space. The covering property is ensured for all n ≥ 2 and the balls are adaptive over a collection of linear spaces.
Adaptive non-asymptotic confidence balls in density estimation
We build confidence balls for the common density s of a real valued sample X1,...,Xn. We use resampling methods to estimate the projection of s onto finite dimensional linear spaces and a model selection procedure to choose an optimal approximation space. The covering property is ensured for all n ≥ 2 and the balls are adaptive over a collection of linear spaces.
An application of classical invariant theory to identifiability in nonparametric mixtures
It is known that the identifiability of multivariate mixtures reduces to a question in algebraic geometry. We solve the question by studying certain generators in the ring of polynomials in vector variables, invariant under the action of the symmetric group.
An approximate necessary condition for the optimal bandwidth selector in kernel density estimation
An approximate necessary condition for the optimal bandwidth choice is derived. This condition is used to construct an iterative bandwidth selector. The algorithm is based on resampling and step-wise fitting the bandwidth to the density estimator from the previous iteration. Examples show fast convergence of the algorithm to the bandwidth value which is surprisingly close to the optimal one no matter what is the initial knowledge on the unknown density.
Analysis of FM demodulator output noise with applications to FM telemetry.
Anisotropic adaptive kernel deconvolution
In this paper, we consider a multidimensional convolution model for which we provide adaptive anisotropic kernel estimators of a signal density measured with additive error. For this, we generalize Fan’s (Ann. Statist.19(3) (1991) 1257–1272) estimators to multidimensional setting and use a bandwidth selection device in the spirit of Goldenshluger and Lepski’s (Ann. Statist.39(3) (2011) 1608–1632) proposal for density estimation without noise. We consider first the pointwise setting and then, we...
Aplicación de la suavización no paramétrica del tipo "K-puntos próximos" a modelos de regresión lineal.
En el modelo de regresión lineal y = E(Y/X = x) = θx, donde (X,Y) es un vector aleatorio bidimensional, del que se dispone de una muestra {(X1, Y1), ..., (Xn, Yn)}, se han introducido recientemente una clase general de estimadores para θ definida como aquellos valores que minimizan el funcional:ψ(θ) = ∫ (αn(x) - θx)2 dΩn(x)donde αn es un estimador no paramétrico del tipo núcleo o histograma para α(x) = E(Y/X = x) y Ωn una función de ponderación.En este trabajo se extiende tal estudio cuando inicialmente...
Application of Mazur-Orlicz's theorem in AMISE calculation
An approximation error and an asymptotic formula are given for shift invariant operators of polynomial order ϱ. Density estimators based on shift invariant operators are introduced and AMISE is calculated.
Applications of intentionally biased bootstrap methods.
Approximating distribution functions by iterated function systems.
Asymptotic law of the intergrated quadratic errors of kernel density and regression estimators under the conditions of dependence. (Loi asymptotique des erreurs quadratiques intégrées des estimateurs à noyau de la densité et de la régression sous des conditions de dépendance.)
Asymptotic normality in density support estimation.
Asymptotic normality in mixture models
Asymptotic normality in mixture models
We study the estimation of a linear integral functional of a distribution F, using i.i.d. observations which density is a mixture of a family of densities k(.,y) under F. We examine the asymptotic distribution of the estimator obtained by plugging the non parametric maximum likelihood estimator (NPMLE) of F in the functional. A problem here is that usually, the NPMLE does not dominate F. Our main aim here is to show that this can be overcome by considering a convex combination of F and the...
Asymptotic normality of the kernel estimate for the Markovian transition operator
We build a kernel estimator of the Markovian transition operator as an endomorphism on L¹ for some discrete time continuous states Markov processes which satisfy certain additional regularity conditions. The main result deals with the asymptotic normality of the kernel estimator constructed.
Asymptotic study of the density associated to a filter of infinite order. (Étude asymptotique de la densité associée à un filtre d'ordre infini.)
Asymptotic unbiased density estimators
This paper introduces a computationally tractable density estimator that has the same asymptotic variance as the classical Nadaraya-Watson density estimator but whose asymptotic bias is zero. We achieve this result using a two stage estimator that applies a multiplicative bias correction to an oversmooth pilot estimator. Simulations show that our asymptotic results are available for samples as low as n = 50, where we see an improvement of as much as 20% over the traditionnal estimator.
Bayes sharpening of imprecise information
A complete algorithm is presented for the sharpening of imprecise information, based on the methodology of kernel estimators and the Bayes decision rule, including conditioning factors. The use of the Bayes rule with a nonsymmetrical loss function enables the inclusion of different results of an under- and overestimation of a sharp value (real number), as well as minimizing potential losses. A conditional approach allows to obtain a more precise result thanks to using information entered as the...
Bayesian density estimation.