Download or read book A Generalized Quantile Estimator Under Censoring written by Y. L. Lio and published by . This book was released on 1987 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Quantile Regression with Censored Data Using Generalized L1 Minimization written by Anna Lindgren and published by . This book was released on 1993 with total page 47 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Some Convergence Results for Kernel Type Quantile Estimators Under Censoring written by Y. L. Lio and published by . This book was released on 1985 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Least Absolute Deviations written by P- Bloomfield and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: Least squares is probably the best known method for fitting linear models and by far the most widely used. Surprisingly, the discrete L 1 analogue, least absolute deviations (LAD) seems to have been considered first. Possibly the LAD criterion was forced into the background because of the com putational difficulties associated with it. Recently there has been a resurgence of interest in LAD. It was spurred on by work that has resulted in efficient al gorithms for obtaining LAD fits. Another stimulus came from robust statistics. LAD estimates resist undue effects from a feyv, large errors. Therefore. in addition to being robust, they also make good starting points for other iterative, robust procedures. The LAD criterion has great utility. LAD fits are optimal for linear regressions where the errors are double exponential. However they also have excellent properties well outside this narrow context. In addition they are useful in other linear situations such as time series and multivariate data analysis. Finally, LAD fitting embodies a set of ideas that is important in linear optimization theory and numerical analysis. viii PREFACE In this monograph we will present a unified treatment of the role of LAD techniques in several domains. Some of the material has appeared in recent journal papers and some of it is new. This presentation is organized in the following way. There are three parts, one for Theory, one for Applicatior.s and one for Algorithms.
Download or read book Counting Processes and Survival Analysis written by Thomas R. Fleming and published by John Wiley & Sons. This book was released on 2011-09-20 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. "The book is a valuable completion of the literature in this field. It is written in an ambitious mathematical style and can be recommended to statisticians as well as biostatisticians." -Biometrische Zeitschrift "Not many books manage to combine convincingly topics from probability theory over mathematical statistics to applied statistics. This is one of them. The book has other strong points to recommend it: it is written with meticulous care, in a lucid style, general results being illustrated by examples from statistical theory and practice, and a bunch of exercises serve to further elucidate and elaborate on the text." -Mathematical Reviews "This book gives a thorough introduction to martingale and counting process methods in survival analysis thereby filling a gap in the literature." -Zentralblatt für Mathematik und ihre Grenzgebiete/Mathematics Abstracts "The authors have performed a valuable service to researchers in providing this material in [a] self-contained and accessible form. . . This text [is] essential reading for the probabilist or mathematical statistician working in the area of survival analysis." -Short Book Reviews, International Statistical Institute Counting Processes and Survival Analysis explores the martingale approach to the statistical analysis of counting processes, with an emphasis on the application of those methods to censored failure time data. This approach has proven remarkably successful in yielding results about statistical methods for many problems arising in censored data. A thorough treatment of the calculus of martingales as well as the most important applications of these methods to censored data is offered. Additionally, the book examines classical problems in asymptotic distribution theory for counting process methods and newer methods for graphical analysis and diagnostics of censored data. Exercises are included to provide practice in applying martingale methods and insight into the calculus itself.
Download or read book On the Asymptotic Properties of a Kernel Type Quantile Estimator from Censored Samples written by Y. O. Lio and published by . This book was released on 1985 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Two step Quantile Estimation of the Censored Regression Model written by James Powell and published by . This book was released on 1986 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Kernel Type Estimator of a Quantile Function from Right Censored Data written by W. J. Padgett and published by . This book was released on 1984 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A Simulation Study of Some Nonparametric Quantile Estimators Under Censoring written by Michelle Elaine Skelton and published by . This book was released on 1989 with total page 74 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1991 with total page 602 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On the Mean Squared Error of Nonparametric Quantile Estimators Under Random Right Censorship written by Y. L. Lio and published by . This book was released on 1986 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt: For randomly right-censored data, new asymptotic expressions for the mean squared errors of the product-limit quantile estimator and a kernel-type quantile estimator are presented in this paper. From these results a comparison of the two quantile estimators with respect to their mean squared errors is given. (Author).
Download or read book Quantile Regression With Censored Data written by and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Quantile Regression written by Cristina Davino and published by John Wiley & Sons. This book was released on 2013-10-24 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: A guide to the implementation and interpretation of Quantile Regression models This book explores the theory and numerous applications of quantile regression, offering empirical data analysis as well as the software tools to implement the methods. The main focus of this book is to provide the reader with a comprehensive description of the main issues concerning quantile regression; these include basic modeling, geometrical interpretation, estimation and inference for quantile regression, as well as issues on validity of the model, diagnostic tools. Each methodological aspect is explored and followed by applications using real data. Quantile Regression: Presents a complete treatment of quantile regression methods, including, estimation, inference issues and application of methods. Delivers a balance between methodolgy and application Offers an overview of the recent developments in the quantile regression framework and why to use quantile regression in a variety of areas such as economics, finance and computing. Features a supporting website (www.wiley.com/go/quantile_regression) hosting datasets along with R, Stata and SAS software code. Researchers and PhD students in the field of statistics, economics, econometrics, social and environmental science and chemistry will benefit from this book.
Download or read book Handbook of Quantile Regression written by Roger Koenker and published by CRC Press. This book was released on 2017-10-12 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantile regression constitutes an ensemble of statistical techniques intended to estimate and draw inferences about conditional quantile functions. Median regression, as introduced in the 18th century by Boscovich and Laplace, is a special case. In contrast to conventional mean regression that minimizes sums of squared residuals, median regression minimizes sums of absolute residuals; quantile regression simply replaces symmetric absolute loss by asymmetric linear loss. Since its introduction in the 1970's by Koenker and Bassett, quantile regression has been gradually extended to a wide variety of data analytic settings including time series, survival analysis, and longitudinal data. By focusing attention on local slices of the conditional distribution of response variables it is capable of providing a more complete, more nuanced view of heterogeneous covariate effects. Applications of quantile regression can now be found throughout the sciences, including astrophysics, chemistry, ecology, economics, finance, genomics, medicine, and meteorology. Software for quantile regression is now widely available in all the major statistical computing environments. The objective of this volume is to provide a comprehensive review of recent developments of quantile regression methodology illustrating its applicability in a wide range of scientific settings. The intended audience of the volume is researchers and graduate students across a diverse set of disciplines.
Download or read book Improving American River Flood Frequency Analyses written by Committee on American River Flood Frequencies and published by National Academies Press. This book was released on 1999-05-12 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sacramento, California, has grown literally at the edge of the Sacramento and American Rivers and for 150 years has struggled to protect itself from periodic floods by employing structural and land management measures. Much of the population lives behind levees, and most of the city's downtown business and government area is vulnerable to flooding. A major flood in 1986 served as impetus for efforts by federal, state, and local entities to identify an acceptable and feasible set of measures to increase Sacramento's level of safety from American River floods. Numerous options were identified in 1991 by the U.S. Army Corps of Engineers (USACE) in a report known as the American River Watershed Investigation. Due to the controversial nature of many of the alternatives identified in that report, study participants were not able to reach consensus on any of the flood control options. In response, the Congress directed the USACE to reevaluate available flood control options and, at the same time, asked the USACE to engage the National Research Council (NRC) as an independent advisor on these difficult studies. In 1995 NRC's Committee on Flood Control Alternatives in the American River Basin issued Flood Risk Management and the American River Basin: An Evaluation. This report outlined an approach for improving the selection of a flood risk reduction strategy from the many available.
Download or read book Advances in Contemporary Statistics and Econometrics written by Abdelaati Daouia and published by Springer Nature. This book was released on 2021-06-14 with total page 713 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a unique collection of contributions on modern topics in statistics and econometrics, written by leading experts in the respective disciplines and their intersections. It addresses nonparametric statistics and econometrics, quantiles and expectiles, and advanced methods for complex data, including spatial and compositional data, as well as tools for empirical studies in economics and the social sciences. The book was written in honor of Christine Thomas-Agnan on the occasion of her 65th birthday. Given its scope, it will appeal to researchers and PhD students in statistics and econometrics alike who are interested in the latest developments in their field.
