Sample density as the function-estimate of population's distribution
Segmentation of the Poisson and negative binomial rate models: a penalized estimator
We consider the segmentation problem of Poisson and negative binomial (i.e. overdispersed Poisson) rate distributions. In segmentation, an important issue remains the choice of the number of segments. To this end, we propose a penalized -likelihood estimator where the penalty function is constructed in a non-asymptotic context following the works of L. Birgé and P. Massart. The resulting estimator is proved to satisfy an oracle inequality. The performances of our criterion is assessed using simulated...
Semiparametric deconvolution with unknown noise variance
This paper deals with semiparametric convolution models, where the noise sequence has a gaussian centered distribution, with unknown variance. Non-parametric convolution models are concerned with the case of an entirely known distribution for the noise sequence, and they have been widely studied in the past decade. The main property of those models is the following one: the more regular the distribution of the noise is, the worst the rate of convergence for the estimation of the signal’s density...
Semiparametric deconvolution with unknown noise variance
This paper deals with semiparametric convolution models, where the noise sequence has a Gaussian centered distribution, with unknown variance. Non-parametric convolution models are concerned with the case of an entirely known distribution for the noise sequence, and they have been widely studied in the past decade. The main property of those models is the following one: the more regular the distribution of the noise is, the worst the rate of convergence for the estimation of the signal's density...
Semiparametric estimation in autoregressive processes with Markov regime. (Estimación semiparamétrica en procesos autorregresivos con régimen de Markov.)
Sequential estimation of survival functions with a neutral to the right process prior
In this work, a parametric sequential estimation method of survival functions is proposed in the Bayesian nonparametric context when neutral to the right processes are used. It is proved that the mentioned method is an 1-SLA rule when Dirichlet processes are used; furthermore, asymptotically pointwise optimal procedures are obtained. Finally, an example is given.
Set estimation under convexity type assumptions
Simple estimators of the parameters of generalized Tukey’s -family
Smoothing and preservation of irregularities using local linear fitting
For nonparametric estimation of a smooth regression function, local linear fitting is a widely-used method. The goal of this paper is to briefly review how to use this method when the unknown curve possibly has some irregularities, such as jumps or peaks, at unknown locations. It is then explained how the same basic method can be used when estimating unsmooth probability densities and conditional variance functions.
Smoothing Histograms by Means of Lattice- and Continuous Distributions.
Some adaptive estimators for slope parameter
An adaptive estimator (of a slope parameter) based on rank statistics is constructed and its asymptotic optimality is studied. A complete orthonormal system is incorporated in the adaptive determination of the score generating function. The proposed sequential procedure is based on a suitable stopping rule. Various properties of the sequential adaptive procedure and the stopping rule are studied. Asymptotic linearity results of linear rank statistics are also studied and some rates of the convergence...
Some applications of probability generating function based methods to statistical estimation
After recalling previous work on probability generating functions for real valued random variables we extend to these random variables uniform laws of large numbers and functional limit theorem for the empirical probability generating function. We present an application to the study of continuous laws, namely, estimation of parameters of Gaussian, gamma and uniform laws by means of a minimum contrast estimator that uses the empirical probability generating function of the sample. We test the procedure...
Some recent results on the law of the iterated logarithm for Banach space valued random variables
Spatial prediction of the mark of a location-dependent marked point process: How the use of a parametric model may improve prediction
We discuss the prediction of a spatial variable of a multivariate mark composed of both dependent and explanatory variables. The marks are location-dependent and they are attached to a point process. We assume that the marks are assigned independently, conditionally on an unknown underlying parametric field. We compare (i) the classical non-parametric Nadaraya-Watson kernel estimator based on the dependent variable (ii) estimators obtained under an assumption of local parametric model where explanatory...
Spatially adaptive density estimation by localised Haar projections
Given a random sample from some unknown density we devise Haar wavelet estimators for with variable resolution levels constructed from localised test procedures (as in Lepski, Mammen and Spokoiny (Ann. Statist.25(1997) 927–947)). We show that these estimators satisfy an oracle inequality that adapts to heterogeneous smoothness of , simultaneously for every point in a fixed interval, in sup-norm loss. The thresholding constants involved in the test procedures can be chosen in practice under...
Statistical inference for fault detection: a complete algorithm based on kernel estimators
This article presents a new concept for a statistical fault detection system, including the detection, diagnosis, and prediction of faults. Theoretical material has been collected to provide a complete algorithm making possible the design of a usable system for statistical inference on the basis of the current value of a symptom vector. The use of elements of artificial intelligence enables self-correction and adaptation to changing conditions. The mathematical apparatus is founded on the methodology...
Strong consistency of regression function estimates
Strong uniform consistency rates of some characteristics of the conditional distribution estimator in the functional single-index model
The aim of this paper is to establish a nonparametric estimate of some characteristics of the conditional distribution. Kernel type estimators for the conditional cumulative distribution function and for the successive derivatives of the conditional density of a scalar response variable Y given a Hilbertian random variable X are introduced when the observations are linked with a single-index structure. We establish the pointwise almost complete convergence and the uniform almost complete convergence...
Suavización no paramétrica en fiabilidad.
En este trabajo consideramos estimaciones no paramétricas de las funciones de razón de fallo y supervivencia en fiabilidad haciendo uso de suavizaciones no paramétricas de la función de distribución empírica (datos no censurados) y de la distribución de Kaplan-Meier (datos censurados). Se obtienen sesgos, varianzas y distribuciones asintóticas de los estimadores aquí propuestos probándose mediante técnicas de expansiones de segundo orden la eficiencia de éstos respecto de otras estimaciones introducidas...
Sur la convergence L1 et L∞ de l'estimateur de la partition aléatoire pour une densité