Download or read book Smooth Nonparametric Quantile Estimation Under Censoring Simulations and Bootstrap Methods written by W. J. Padgett and published by . This book was released on 1986 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A Smooth Nonparametric Quantile Estimator from Right Censored Data written by W. J. Padgett and published by . This book was released on 1987 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).
Download or read book Smooth Quantile Processes for Right Censored Data written by Katsuhiro Uechi and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1991 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bootstrap Methods written by Michael R. Chernick and published by John Wiley & Sons. This book was released on 2011-09-23 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: A practical and accessible introduction to the bootstrap method——newly revised and updated Over the past decade, the application of bootstrap methods to new areas of study has expanded, resulting in theoretical and applied advances across various fields. Bootstrap Methods, Second Edition is a highly approachable guide to the multidisciplinary, real-world uses of bootstrapping and is ideal for readers who have a professional interest in its methods, but are without an advanced background in mathematics. Updated to reflect current techniques and the most up-to-date work on the topic, the Second Edition features: The addition of a second, extended bibliography devoted solely to publications from 1999–2007, which is a valuable collection of references on the latest research in the field A discussion of the new areas of applicability for bootstrap methods, including use in the pharmaceutical industry for estimating individual and population bioequivalence in clinical trials A revised chapter on when and why bootstrap fails and remedies for overcoming these drawbacks Added coverage on regression, censored data applications, P-value adjustment, ratio estimators, and missing data New examples and illustrations as well as extensive historical notes at the end of each chapter With a strong focus on application, detailed explanations of methodology, and complete coverage of modern developments in the field, Bootstrap Methods, Second Edition is an indispensable reference for applied statisticians, engineers, scientists, clinicians, and other practitioners who regularly use statistical methods in research. It is also suitable as a supplementary text for courses in statistics and resampling methods at the upper-undergraduate and graduate levels.
Download or read book Smooth Nonparametric Quantile Estimation from Right censored Data written by Yuhlong Lio and published by . This book was released on 1987 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Jackknife and Bootstrap written by Jun Shao and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: The jackknife and bootstrap are the most popular data-resampling meth ods used in statistical analysis. The resampling methods replace theoreti cal derivations required in applying traditional methods (such as substitu tion and linearization) in statistical analysis by repeatedly resampling the original data and making inferences from the resamples. Because of the availability of inexpensive and fast computing, these computer-intensive methods have caught on very rapidly in recent years and are particularly appreciated by applied statisticians. The primary aims of this book are (1) to provide a systematic introduction to the theory of the jackknife, the bootstrap, and other resampling methods developed in the last twenty years; (2) to provide a guide for applied statisticians: practitioners often use (or misuse) the resampling methods in situations where no theoretical confirmation has been made; and (3) to stimulate the use of the jackknife and bootstrap and further devel opments of the resampling methods. The theoretical properties of the jackknife and bootstrap methods are studied in this book in an asymptotic framework. Theorems are illustrated by examples. Finite sample properties of the jackknife and bootstrap are mostly investigated by examples and/or empirical simulation studies. In addition to the theory for the jackknife and bootstrap methods in problems with independent and identically distributed (Li.d.) data, we try to cover, as much as we can, the applications of the jackknife and bootstrap in various complicated non-Li.d. data problems.
Download or read book Nonparametric Estimation of Quantiles and of Density Functions Under Censoring Discrete Failure Models and Multiple Comparisons written by W. J. Padgett and published by . This book was released on 1985 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Journal of the American Statistical Association written by and published by . This book was released on 1999 with total page 1584 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Simple Nonparametric Approach for Estimation and Inference of Conditional Quantile Functions written by Zheng Fang and published by . This book was released on 2018 with total page 53 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we present a new nonparametric method for estimating a conditional quantile function and develop its weak convergence theory. The proposed estimator is computationally easy-to-implement, and automatically ensures quantile monotonicity by construction. For inference, we propose to use a residual bootstrap method. The Monte Carlo simulations show that our new estimator compares well with the checkfunction-based estimator in terms of estimation mean squared error (MSE), and the bootstrap confidence bands give adequate coverage probabilities. An empirical example considering a dataset from Canadian high school graduate earnings illustrates that the proposed method delivers a more reasonable quantile estimate than the check-function counterpart.
Download or read book Lattice Structures in the Bootstrap and Nonparametric Bootstrap Inference for Censored Data written by Horng-Shing Lu and published by . This book was released on 1990 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bootstrap Methods and Their Application written by A. C. Davison and published by Cambridge University Press. This book was released on 1997-10-28 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt: Disk contains the library functions and documentation for use with Splus for Windows.
Download or read book Research in Progress written by and published by . This book was released on 1984 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Statistical Theory and Method Abstracts written by and published by . This book was released on 2001 with total page 756 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Government Reports Announcements Index written by and published by . This book was released on 1987 with total page 902 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nonparametric Curve Estimation written by Sam Efromovich and published by Springer Science & Business Media. This book was released on 1999-08-05 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a systematic, comprehensive, and unified account of modern nonparametric statistics of density estimation, nonparametric regression, filtering signals, and time series analysis. The companion software package, available over the Internet, brings all of the discussed topics into the realm of interactive research. Virtually every claim and development mentioned in the book is illustrated with graphs which are available for the reader to reproduce and modify, making the material fully transparent and allowing for complete interactivity.
Download or read book A Simulation Comparison of Parametric and Nonparametric Estimators of Quantiles from Right Censored Data written by Shyamalee Kumary Serasinghe and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantiles are useful in describing distributions of component lifetimes. Data, consisting of the lifetimes of sample units, used to estimate quantiles are often censored. Right censoring, the setting investigated here, occurs, for example, when some test units may still be functioning when the experiment is terminated. This study investigated and compared the performance of parametric and nonparametric estimators of quantiles from right censored data generated from Weibull and Lognormal distributions, models which are commonly used in analyzing lifetime data. Parametric quantile estimators based on these assumed models were compared via simulation to each other and to quantile estimators obtained from the nonparametric Kaplan- Meier Estimator of the survival function. Various combinations of quantiles, censoring proportion, sample size, and distributions were considered. Our simulation show that the larger the sample size and the lower the censoring rate the better the performance of the estimates of the 5th percentile of Weibull data. The lognormal data are very sensitive to the censoring rate and we observed that for higher censoring rates the incorrect parametric estimates perform the best. If you do not know the underlying distribution of the data, it is risky to use parametric estimates of quantiles close to one. A limitation in using the nonparametric estimator of large quantiles is their instability when the censoring rate is high and the largest observations are censored. Key Words: Quantiles, Right Censoring, Kaplan-Meier estimator.
