An approach of the Naive Bayes classifier for the document classification.
An expectation maximization algorithm to model failure times by continuous-time Markov chains.
Apollo 13 Risk Assessment Revisited
Fault tree methodology is the most widespread risk assessment tool by which one is able to predict - in principle - the outcome of an event whenever it is reduced to simpler ones by the logic operations conjunction and disjunction according to the basics of Boolean algebra. The object of this work is to present an algorithm by which, using the corresponding computer code, one is able to predict - in practice - the outcome of an event whenever its fault tree is given in the usual form.
Application of MCMC to change point detection
A nonstandard approach to change point estimation is presented in this paper. Three models with random coefficients and Bayesian approach are used for modelling the year average temperatures measured in Prague Klementinum. The posterior distribution of the change point and other parameters are estimated from the random samples generated by the combination of the Metropolis-Hastings algorithm and the Gibbs sampler.
Approximated maximum likelihood estimation of parameters of discrete stable family
In this article we propose a method of parameters estimation for the class of discrete stable laws. Discrete stable distributions form a discrete analogy to classical stable distributions and share many interesting properties with them such as heavy tails and skewness. Similarly as stable laws discrete stable distributions are defined through characteristic function and do not posses a probability mass function in closed form. This inhibits the use of classical estimation methods such as maximum...
Arithmetizing continuous distributions: numerical aspects.
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 and Frequentist Two-Sample Predictions of the Inverse Weibull Model Based on Generalized Order Statistics
2000 Mathematics Subject Classification: 62E16,62F15, 62H12, 62M20.This paper is concerned with the problem of deriving Bayesian prediction bounds for the future observations (two-sample prediction) from the inverse Weibull distribution based on generalized order statistics (GOS). Study the two side interval Bayesian prediction, point prediction under symmetric and asymmetric loss functions and the maximum likelihood (ML) prediction using "plug-in" procedure for future observations from the inverse...
Bayesian approach for joint longitudinal and time-to-event data with survival fraction.
Bayesian Prediction of Weibull Distribution Based on Fixed and Random Sample Size
2000 Mathematics Subject Classification: 62E16, 65C05, 65C20.We consider the problem of predictive interval for future observations from Weibull distribution. We consider two cases they are: (i) fixed sample size (FSS), (ii) random sample size (RSS). Further, we derive the predictive function for both FSS and RSS in closed forms. Next, the upper and lower 1%, 2.5%, 5% and 10% critical points for the predictive functions are calculated. To show the usefulness of our results, we present some simulation...
Binary segmentation and Bonferroni-type bounds
We introduce the function , where and are the pdf and cdf of , respectively. We derive two recurrence formulas for the effective computation of its values. We show that with an algorithm for this function, we can efficiently compute the second-order terms of Bonferroni-type inequalities yielding the upper and lower bounds for the distribution of a max-type binary segmentation statistic in the case of small samples (where asymptotic results do not work), and in general for max-type random variables...
Calculus of the estimators of linear quantile regression by the method ACCPM.
Censored regression models with double exponential error distributions: an iterattive estimation procedure based on medians for correcting bias.
In this paper, we consider a simple iterative estimation procedure for censored regression models with symmetrical exponential error distributions. Although each step requires to impute the censored data with conditional medians, its tractability is guaranteed as well as its convergence at geometrical rate. Finally, as the final estimate coincides with a Huber M-estimator, its consistency and asymptotic normality are easily proved.
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...
Checking proportional rates in the two-sample transformation model
Transformation models for two samples of censored data are considered. Main examples are the proportional hazards and proportional odds model. The key assumption of these models is that the ratio of transformation rates (e. g., hazard rates or odds rates) is constant in time. A~method of verification of this proportionality assumption is developed. The proposed procedure is based on the idea of Neyman's smooth test and its data-driven version. The method is suitable for detecting monotonic as well...
Choosing the best -divergence goodness-of-fit statistic in multinomial sampling with linear constraints
In this paper we present a simulation study to analyze the behavior of the -divergence test statistics in the problem of goodness-of-fit for loglinear models with linear constraints and multinomial sampling. We pay special attention to the Rényi’s and -divergence measures.
Colinéarité et instabilité numérique dans le modèle linéaire
Colinearité et Instabilité Numérique dans le Modèle Linéaire
In this paper we give the expression of the multiple correlation coefficient in a linear model according to the coefficients of correlation. This expression makes it possible to analyze from a numerical point of view the instability of estimates in the case of collinear explanatory variables in the linear model or in the autoregressive model. This numerical approach, that we show on two examples, thus supplements the usual approach of the quasi colinearity, founded on the statistical properties...
Combining forecasts using the least trimmed squares
Employing recently derived asymptotic representation of the least trimmed squares estimator, the combinations of the forecasts with constraints are studied. Under assumption of unbiasedness of individual forecasts it is shown that the combination without intercept and with constraint imposed on the estimate of regression coefficients that they sum to one, is better than others. A numerical example is included to support theoretical conclusions.