12,680 research outputs found
Consistency of the generalized MLE of a joint distribution function with multivariate interval-censored data
AbstractWong and Yu [Generalized MLE of a joint distribution function with multivariate interval-censored data, J. Multivariate Anal. 69 (1999) 155â166] discussed generalized maximum likelihood estimation of the joint distribution function of a multivariate random vector whose coordinates are subject to interval censoring. They established uniform consistency of the generalized MLE (GMLE) of the distribution function under the assumption that the random vector is independent of the censoring vector and that both of the vector distributions are discrete. We relax these assumptions and establish consistency results of the GMLE under a multivariate mixed case interval censorship model. van der Vaart and Wellner [Preservation theorems for GlivenkoâCantelli and uniform GlivenkoâCantelli class, in: E. Gine, D.M. Mason, J.A. Wellner (Eds.), High Dimensional Probability, vol. II, BirkhĂ€user, Boston, 2000, pp. 115â133] and Yu [Consistency of the generalized MLE with multivariate mixed case interval-censored data, Ph.D Dissertation, Binghamton University, 2000] independently proved strong consistency of the GMLE in the L1(ÎŒ)-topology, where ÎŒ is a measure derived from the joint distribution of the censoring variables. We establish strong consistency of the GMLE in the topologies of weak convergence and pointwise convergence, and eventually uniform convergence under appropriate distributional assumptions and regularity conditions
Estimation of Stress-Strength model in the Generalized Linear Failure Rate Distribution
In this paper, we study the estimation of , also so-called the
stress-strength model, when both and are two independent random
variables with the generalized linear failure rate distributions, under
different assumptions about their parameters. We address the maximum likelihood
estimator (MLE) of and the associated asymptotic confidence interval. In
addition, we compute the MLE and the corresponding Bootstrap confidence
interval when the sample sizes are small. The Bayes estimates of and the
associated credible intervals are also investigated. An extensive computer
simulation is implemented to compare the performances of the proposed
estimators. Eventually, we briefly study the estimation of this model when the
data obtained from both distributions are progressively type-II censored. We
present the MLE and the corresponding confidence interval under three different
progressive censoring schemes. We also analysis a set of real data for
illustrative purpose.Comment: 31 pages, 2 figures, preprin
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Inference under progressively type II right censored sampling for certain lifetime distributions
In this paper, estimation of the parameters of a certain family of two-parameter lifetime
distributions based on progressively Type II right censored samples (including ordinary Type II right censoring) is studied. This family, of reverse hazard distributions, includes the Weibull, Gompertz and Lomax distributions. A new type of parameter estimation, named inverse estimation, is introduced for both parameters. Exact confidence intervals for one of the parameters and generalized confidence intervals for the other are explored; inference for the first parameter can be accomplished by our
methodology independently of the unknown value of the other parameter in this family of distributions. Derivation of the estimation method uses properties of order statistics.
A simulation study in the particular context of the Weibull distribution illustrates the accuracy of these confidence intervals and compares inverse estimators favorably with maximum likelihood estimators. A numerical example is used to illustrate the proposed procedures
A nonparametric model-based estimator for the cumulative distribution function of a right censored variable in a finite population
In survey analysis, the estimation of the cumulative distribution function
(cdf) is of great interest: it allows for instance to derive quantiles
estimators or other non linear parameters derived from the cdf. We consider the
case where the response variable is a right censored duration variable. In this
framework, the classical estimator of the cdf is the Kaplan-Meier estimator. As
an alternative, we propose a nonparametric model-based estimator of the cdf in
a finite population. The new estimator uses auxiliary information brought by a
continuous covariate and is based on nonparametric median regression adapted to
the censored case. The bias and variance of the prediction error of the
estimator are estimated by a bootstrap procedure adapted to censoring. The new
estimator is compared by model-based simulations to the Kaplan-Meier estimator
computed with the sampled individuals: a significant gain in precision is
brought by the new method whatever the size of the sample and the censoring
rate. Welfare duration data are used to illustrate the new methodology.Comment: 18 pages, 5 figure
Statistics of extremes under random censoring
We investigate the estimation of the extreme value index when the data are
subject to random censorship. We prove, in a unified way, detailed asymptotic
normality results for various estimators of the extreme value index and use
these estimators as the main building block for estimators of extreme
quantiles. We illustrate the quality of these methods by a small simulation
study and apply the estimators to medical data.Comment: Published in at http://dx.doi.org/10.3150/07-BEJ104 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
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