Consistency of a Nonparametric Estimation of a Density Functional.
Consistency of Estimators of Cyclic Functional Parameters for Some Nonstationary Processes
Contribution to Nonparametric Generalized Failure Rate Function Estimation
Correction to 'Estimating median and other quantiles in nonparametric models' (Applicationes Math. 23 (3) (1995), 363–370)
Corrections : «Estimation des densités : risque minimax»
Cramer Type Large Deviations for Studentized U-Statistics.
¿Cuántos clusters hay en una población?
Sea una población cerrada formada por un número desconocido K y finito de clusters. El método bootstrap es utilizado para estimar el número de clusters que constituyen una población. Se propone un estimador para K, el cual es ajustado y corregido por su sesgo estimado mediante el método bootstrap de Efron (1979). La varianza del "estimador bootstrap" se calcula por el método jackknife agrupado. Mediante simulación, el estimador es comparado con el de Bickel y Yavah (1985).
Density Estimates of Discriminant Functions
Density smoothness estimation problem using a wavelet approach
In this paper we consider a smoothness parameter estimation problem for a density function. The smoothness parameter of a function is defined in terms of Besov spaces. This paper is an extension of recent results (K. Dziedziul, M. Kucharska, B. Wolnik, Estimation of the smoothness parameter). The construction of the estimator is based on wavelets coefficients. Although we believe that the effective estimation of the smoothness parameter is impossible in general case, we can show that it becomes...
Dependent Gaussian samples: estimation of the scatter uniform in dimension.
Deviation inequalities and moderate deviations for estimators of parameters in bifurcating autoregressive models
The purpose of this paper is to investigate the deviation inequalities and the moderate deviation principle of the least squares estimators of the unknown parameters of general th-order asymmetric bifurcating autoregressive processes, under suitable assumptions on the driven noise of the process. Our investigation relies on the moderate deviation principle for martingales.
Discrimination binaire non paramétrique. Méthodes d'estimation du paramètre de lissage
Drift estimation from -mixing sequences.
Efficacités comparées de certaines méthodes de prédiction pour un ARMA perturbé
Efficient estimation of functionals of the spectral density of stationary Gaussian fields
Minimax bounds for the risk function of estimators of functionals of the spectral density of Gaussian fields are obtained. This result is a generalization of a previous result of Khas'minskii and Ibragimov on Gaussian processes. Efficient estimators are then constructed for these functionals. In the case of linear functionals these estimators are given for all dimensions. For non-linear integral functionals, these estimators are constructed for the two and three dimensional problems.
Efficient estimation of functionals of the spectral density of stationary gaussian fields
Efficient estimation under constraints
Efficient robust nonparametric estimation in a semimartingale regression model
The paper considers the problem of robust estimating a periodic function in a continuous time regression model with the dependent disturbances given by a general square integrable semimartingale with an unknown distribution. An example of such a noise is a non-Gaussian Ornstein–Uhlenbeck process with jumps (see (J. R. Stat. Soc. Ser. B Stat. Methodol.63 (2001) 167–241), (Ann. Appl. Probab.18 (2008) 879–908)). An adaptive model selection procedure, based on the weighted least square estimates, is...
Empirical comparison between the Nelson-Aalen Estimator and the Naive Local Constant Estimator.
The Nelson-Aalen estimator is widely used in biostatistics as a non-parametric estimator of the cumulative hazard function based on a right censored sample. A number of alternative estimators can be mentioned, namely, the naive local constant estimator (Guillén, Nielsen and Pérez-Marín, 2007) which provides improved bias versus variance properties compared to the traditional Nelson-Aalen estimator. Nevertheless, an empirical comparison of these two estimators has never been carried out. In this...
Empirical estimator of the regularity index of a probability measure
The index of regularity of a measure was introduced by Beirlant, Berlinet and Biau [1] to solve practical problems in nearest neighbour density estimation such as removing bias or selecting the number of neighbours. These authors proved the weak consistency of an estimator based on the nearest neighbour density estimator. In this paper, we study an empirical version of the regularity index and give sufficient conditions for its weak and strong convergence without assuming absolute continuity or...