Smooth Nonparametric Quantile Estimation from Right-censored Data PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Smooth Nonparametric Quantile Estimation from Right-censored Data PDF full book. Access full book title Smooth Nonparametric Quantile Estimation from Right-censored Data by Yuhlong Lio. Download full books in PDF and EPUB format.
Author: Yuhlong Lio
Publisher:
ISBN:
Category : Nonparametric statistics
Languages : en
Pages : 162
Get Book Here
Book Description
Author: Yuhlong Lio
Publisher:
ISBN:
Category : Nonparametric statistics
Languages : en
Pages : 162
Get Book Here
Book Description
Author: W. J. Padgett
Publisher:
ISBN:
Category :
Languages : en
Pages : 25
Get Book Here
Book Description
Based on randomly right-censored data, a smooth nonparametric estimator of the quantile function of the lifetime distribution is studied. The estimator is defined to be the solution x sub n (p) to F sub n (p)) = O, where F sub n is the distribution function corresponding to a kernel estimator of the lifetime density. The strong consistency and asymptotic normality of x sub n (p) are shown. Some simulation results comparing this estimator with the product of the bandwidth required for computing F sub n is investigated using bootstrap methods. Illustrative examples are given. (Author).
Author: W. J. Padgett
Publisher:
ISBN:
Category :
Languages : en
Pages : 29
Get Book Here
Book Description
The objectives of this paper are two-fold. One is to report results of extensive Monte Carlo simulations which demonstrate the behavior of the mean squared error of the kernel estimator with respect to bandwidth. These simulations provide a method of choosing an optimal bandwidth when the form of the lifetime and censoring distributions are known. Also, they compare the kernel-type estimator with the product-limit qauntile estimator. Five commonly used parametric lifetime distributions, two censoring mechanisms, and four different kernel functions are considered in this study, which is an extension of the brief simulations for exponential distributions reported by Padgett (1986). The second objective is to present a nonparametric method for bandwidth selection based on the bootstrap for right-censored data. This data-based procedure used the bootstrap to estimate mean squared error, and is both an extension and modification of the methods proposed by Padgett. Bandwidth selection using the bootstrap is important for small and moderately large samples since no exact expressions exist for the mean squared error of the kernel-type quantile estimator.
Author: Katsuhiro Uechi
Publisher:
ISBN:
Category : Mathematical statistics
Languages : en
Pages :
Get Book Here
Book Description
The development of an estimator of a quantile function Q(p) is discussed. The smooth nonparametric estimator Qn(p) of a quantile function Q(p) is defined as the solution to Fn(Qn(p)) = p, where Fn is a smooth Kaplan-Meier estimator of an unknown continuous distribution function F(x). The asymptotic properties of the smooth quantile process, n(Qn(p) - Q(p)) , based on right censored lifetimes are studied. The asymptotic properties of the bootstrap quantile process, n(Q n(p) - Q(p)) are also investigated and shown to have the same limiting distribution as the smooth quantile process. The bootstrap method to approximate the sampling distribution of the smooth quantile process is used to construct simultaneous confidence bands for a quantile function and the difference of two quantile functions. A Monte Carlo simulation is conducted to assess the performance of these confidence bands by computing the lengths and coverage probabilities of the bands. The optimum bandwidth is also investigated.
Author: W. J. Padgett
Publisher:
ISBN:
Category :
Languages : en
Pages : 13
Get Book Here
Book Description
Major results have been obtained in the areas of nonparametric estimation of quantiles and of density functions under censoring, discrete failure models, and multiple comparisons. In particular, smooth nonparametric estimators of quantile functions from censored data were developed which give better estimates of percentiles of the lifetime distribution than the usual product-limit quantile function. Also, smooth density estimators from censored data were investigated using maximum penalized likelihood procedures. Several parametric models were proposed for the case of discrete failure data. These models provide a better fit to such data than some previously used discrete models. Finally, new methods of constructing simultaneous confidence intervals for pairwise differences of means of normal populations were developed, and the problem of selecting an asymptotically optimal design for comparing several new treatments with a control was solved. Work is continuing on the study of properties of kernel type quantile function estimators and development of goodness-of-fit tests for the model assumptions in accelerated life testing. Keywords: Nonparametric quantile estimation; Density estimation; Right-censored data; Discrete failure models; Multiple comparisons; Accelerated life testing.
Author: K. J. Padgett
Publisher:
ISBN:
Category :
Languages : en
Pages : 15
Get Book Here
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: Y. L. Lio
Publisher:
ISBN:
Category :
Languages : en
Pages : 26
Get Book Here
Book Description
Based on right-censored data from a lifetime distribution F sub 0, a smooth alternative to the product-limit estimator as a nonparametric quantile estimator of a population quantile is proposed. The estimator is a generalized product-limit quantile obtained by averaging appropriate subsample product-limit quantiles over all subsamples of a fixed size. Under the random censorship model and some conditions of F sub 0, it is shown that the estimator is consistent and has the same asymptotic normal distribution as the product-limit quantile estimator performs better than the product-limit quantile estimator in the sense of estimated mean squared errors.
Author:
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 240
Get Book Here
Book Description
Author: Jagadish Purushotham Gogate
Publisher:
ISBN:
Category : Distribution (Probability theory)
Languages : en
Pages : 140
Get Book Here
Book Description
Author: Y. O. Lio
Publisher:
ISBN:
Category :
Languages : en
Pages : 17
Get Book Here
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.
