Bootstrap of a Linear Model with AR-Error Structure.
Bootstraping of M-smoothers
Bootstrapping Rank Statistics.
Bootstrapping the shorth for regression
The paper is concerned with the asymptotic distributions of estimators for the length and the centre of the so-called η-shorth interval in a nonparametric regression framework. It is shown that the estimator of the length converges at the n1/2-rate to a Gaussian law and that the estimator of the centre converges at the n1/3-rate to the location of the maximum of a Brownian motion with parabolic drift. Bootstrap procedures are proposed and shown to be consistent. They are compared with the plug-in...
Bounds on expectations of record range and record increment from distributions with bounded support.
Bounds on the expectations of th record increments.
Box-spline histograms for multivariate density estimation
The uniform approach to calculation of MISE for histogram and density box-spline estimators gives us a possibility to obtain estimators of derivatives of densities and the asymptotic constant.
Cálculo de la distribución del tiempo de vida de componentes mediante autopsia en sistemas binarios aditivos, serie-paralelo y paralelo-serie.
En este artículo se estudia el problema de determinar la función de distribución del tiempo de vida de las componentes de un sistema binario, a partir del conocimiento de las leyes que rigen el funcionamiento del sistema y del conjunto de componentes que causa su fallo (obtenida mediante autopsia del sistema en el momento de su deterioro).Se presentan los resultados de Meilijson (1981) y Nowik (1990) que proponen un sistema de ecuaciones implícito para obtener estas distribuciones. Sin embargo,...
Central limit theorem for square error of multivariate nonparametric box spline density estimators
We prove the central limit theorem for the integrated square error of multivariate box-spline density estimators.
Challenging the empirical mean and empirical variance: A deviation study
We present new M-estimators of the mean and variance of real valued random variables, based on PAC-Bayes bounds. We analyze the non-asymptotic minimax properties of the deviations of those estimators for sample distributions having either a bounded variance or a bounded variance and a bounded kurtosis. Under those weak hypotheses, allowing for heavy-tailed distributions, we show that the worst case deviations of the empirical mean are suboptimal. We prove indeed that for any confidence level, there...
Change Point Tests Based on U-Statistics with Applications in Reliability.
Change-point estimation from indirect observations. 1. Minimax complexity
We consider the problem of nonparametric estimation of signal singularities from indirect and noisy observations. Here by singularity, we mean a discontinuity (change-point) of the signal or of its derivative. The model of indirect observations we consider is that of a linear transform of the signal, observed in white noise. The estimation problem is analyzed in a minimax framework. We provide lower bounds for minimax risks and propose rate-optimal estimation procedures.
Change-point estimation from indirect observations. 2. Adaptation
We focus on the problem of adaptive estimation of signal singularities from indirect and noisy observations. A typical example of such a singularity is a discontinuity (change-point) of the signal or of its derivative. We develop a change-point estimator which adapts to the unknown smoothness of a nuisance deterministic component and to an unknown jump amplitude. We show that the proposed estimator attains optimal adaptive rates of convergence. A simulation study demonstrates reasonable practical...
Change-point problems: A Bayesian nonparametric approach
A change-point problem is examined from a Bayesian viewpoint, under nonparametric hypotheses. A Ferguson-Dirichlet prior is chosen and the posterior distribution is computed for the change-point and for the unknown distribution functions.
Characteristic properties of generalized order statistics from exponential distributions
Exponential distributions are characterized by distributional properties of generalized order statistics. These characterizations include known results for ordinary order statistics and record values as particular cases.
Characterizations of distributions by moments of order statistics when the sample size is random
We give characterizations of the uniform distribution in terms of moments of order statistics when the sample size is random. Special cases of a random sample size (logarithmic series, geometrical, binomial, negative binomial, and Poisson distribution) are also considered.
Characterizations of Distributions Via Two Expected Values of Order Statistics.
Characterizations of exponential distributions by spacings of generalized order statistics
-3Properties of spacings of generalized order statistics based on IFR and DFR distributions are shown to characterize exponential distributions.
Characterizations of power distributions via moments of order statistics and record values
Power distributions can be characterized by equalities involving three moments of order statistics. Similar equalities involving three moments of k-record values can also be used for such a characterization. The case of samples with random sizes is also considered.
Characterizations of the inverse Weibull distribution and generalized extreme value distributions by moments of kth record values
We give characterization conditions for the inverse Weibull distribution and generalized extreme value distributions by moments of kth record values.