Author: Y. O. Lio
Publisher:
ISBN:
Category :
Languages : en
Pages : 17
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Book Description
In reliability and medical studies, it is often of interest to estimate various quantiles of the unknown lifetime distribution. In particular, the median lifetime and extreme quantiles are of interest to the experimenter in such studies. In many life testing and medical follow-up experiments, however, arbritrarily right-censored data arise, and it is important to be able to estimate the quantiles of interest based on the censored data. For such data, some kernel-type quantile estimators are considered in this paper which give smoother estimates than the usual product-limit quantile function. Keywords: Random right-censorship; Kernel estimation; Product-limit quantile function; Asymptotic normality; and Mean-square convergence.
Author: Y. L. Lio
Publisher:
ISBN:
Category :
Languages : en
Pages : 18
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Book Description
Based on right-censored data from a lifetime distribution, a kernel-type estimator of a certain quantile function is studied. This estimator is smoother than a product-limit quantile function. This document also covers: asymptotic normality; asymptotic mean equivalence; and mean square convergence. Keywords: probability distribution; kernel functions.
Author:
Publisher:
ISBN:
Category : Military research
Languages : en
Pages : 284
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Book Description
Author: K. J. Padgett
Publisher:
ISBN:
Category :
Languages : en
Pages : 15
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Book Description
The main objectives of this research have been the development of smooth nonparametric estimators of quantile functions from right-censored data and the further study of smooth density estimators from censored observations. In particular, kernel-type quantile estimators have been obtained under censoring which give better estimates of percentiles of the lifetime distribution than the usual product-limit quantile estimator. During the past year, asymptotic properties of these kernel quantile estimators have been developed, including asymptotic normality, consistency, and mean square convergence. In addition, a data-based procedure for selecting the bandwidth has been investigated using the bootstrap, and approximate confidence for the true quantile have been proposed using bootstrap estimates of the sampling distribution. Theoretical results on the optimal bandwidth selection for kernel density estimators under random right censorship have also been obtained. New results in several other problem areas were also developed. These included the study of linear empirical Bayes estimators, prediction intervals for the inverse Gaussian distribution, nonparametric hazard rate estimation under censoring, nonparametric inference for step-stress accelerated life tests under censoring, discrete failure models, simultaneous confidence intervals for pairwise differences of normal means, and optimal designs for comparing treatments with a control.
Author: Madan Lal Puri
Publisher: Walter de Gruyter
ISBN: 3110917823
Category : Mathematics
Languages : en
Pages : 760
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Author:
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 240
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Book Description
Author: W. J. Padgett
Publisher:
ISBN:
Category :
Languages : en
Pages : 25
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Book Description
Arbitrarily right-censored data arise naturally in industrial life testing and medical follow-up studies. In these situations it is important to be able to obtain nonparametric estimates of various characteristics of the survival function S. Based on such right-censored data, Kaplan and Meier gave the nonparametric maximum likelihood estimator of S, called the product-limit estimator, and, among others, Reid has proposed methods of estimating the median survival time from the product-limit estimator. Recently, Nair studied the problem of confidence bands for the survival function obtained from the product-limit estimator. Also, Padgett and McNichols and McNichols and Padgett have discussed estimation of a density for the survival distribution based on right-censored data. One characteristic of the survival distribution that is of interest is the quantile function, which is useful in reliability and medical studies. The quantile function of the product-limit estimator is a step function with jumps corresponding to the uncensored observations. The purpose of this paper is to present a smoothed nonparametric estimator of the quantile function from arbitrarily right-censored data based on the kernel method. It will be shown that under general conditions this estimator, mentioned briefly by Parzen is strongly consistent, and based on the results of a small Monte-Carol simulation study, performs better than quantile function of the product-limit estimator in the sense of smaller mean squared error. In particular, better estimates of the median survival time are obtainable. In addition, an approximation to the kernel estimator will be shown to be almost surely asymptotically equivalent to it under certain conditions.
Author: W. J. Padgett
Publisher:
ISBN:
Category :
Languages : en
Pages : 34
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Book Description
The small-sample behavior of two kernel-type density estimators which have been proposed in the literature for randomly right-censored samples is investigated via Monte Carlo simulations. The extensive simulation study was performed for five families of life distributions, two different censoring distributions, three kernel functions, and several bandwidth sequences and for sample sizes from n=20 to n=300. The simulation results reinforce previous theoretical results for the estimators and lead to conjectures about their general behavior asymptotically as well as for small samples. A comparison of the two density estimators is also indicated.
Author:
Publisher:
ISBN:
Category : Mathematical statistics
Languages : en
Pages : 558
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Book Description
Author: W. J. Padgett
Publisher:
ISBN:
Category :
Languages : en
Pages : 21
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Book Description
Right-censored data arise very naturally in life testing and reliability studies. For such data, it is important to be able to obtain good nonparametric estimates of various characteristics of the unknown lifetime distribution. This report concerns the computational procedure for a kernel-type nonparametric estimator of the quantile function of the lifetimne distribution from right-censored data. This estimator was suggested by Padgett (1986), extending the complete sample results of Yang (1985). The large sample properties of the estimator, such as asymptotic normality and mean square convergence, were studied by Lio, Padgett and Yu (1986) and by Lio and Padgett (1985). In this report, a procedure for calculation of the kernel-type quantile estimate from right-censored data is described, and a listing of a computer program in FORTRAN code is provided.
