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 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 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 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 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 Survival Analysis written by John P. Klein and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: Making complex methods more accessible to applied researchers without an advanced mathematical background, the authors present the essence of new techniques available, as well as classical techniques, and apply them to data. Practical suggestions for implementing the various methods are set off in a series of practical notes at the end of each section, while technical details of the derivation of the techniques are sketched in the technical notes. This book will thus be useful for investigators who need to analyse censored or truncated life time data, and as a textbook for a graduate course in survival analysis, the only prerequisite being a standard course in statistical methodology.
Download or read book Quantile Regression written by Cristina Davino and published by John Wiley & Sons. This book was released on 2013-12-31 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 Unified Methods for Censored Longitudinal Data and Causality written by Mark J. van der Laan and published by Springer Science & Business Media. This book was released on 2012-11-12 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: A fundamental statistical framework for the analysis of complex longitudinal data is provided in this book. It provides the first comprehensive description of optimal estimation techniques based on time-dependent data structures. The techniques go beyond standard statistical approaches and can be used to teach masters and Ph.D. students. The text is ideally suitable for researchers in statistics with a strong interest in the analysis of complex longitudinal data.
Download or read book AIDS Epidemiology written by Nicholas P. Jewell and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1974, the Societal Institute of the Mathematical Sciences (SIMS) initiated a series of five-day Research Application Conferences (RAC's) at Alta, Utah, for the purpose of probing in depth societal fields in light of their receptivity to mathematical and statistical analysis. The first eleven conferences addressed ecosystems, epidemiology, energy, environmental health, time series and ecological processes, energy and health, energy conversion and fluid mechanics, environmental epidemiology: risk assessment, atomic bomb survival data: utilization and analysis, modem statistical methods in chronic disease epidemiology and scientific issues in quantitative cancer risk assess ment. These Proceedings are a result of the twelfth conference on Statistical Methodology for Study of the AIDS Epidemic which was held in 1991 at the Mathematical Sciences Research Institute, Berkeley, California. For five days, 45 speakers and observers contributed their expertise in the relevant biology and statistics. The presentations were timely and the discussion was both enlightening and at times spirited. Members of the Program Committee for the Conference were Klaus Dietz (University of Tiibingen, Germany), Vernon T. Farewell (University of Waterloo, Ontario), and Nicholas P. Jewell (University of California, Berke ley) (Chair). The Conference was supported by a grant to SIMS from the National Institute of Drug Abuse. D. L. Thomsen, Jr.
Download or read book A Method for Obtaining Weak Convergence Results for Quantile Processes with Applications to Censored Survival Data written by H. Doss and published by . This book was released on 1990 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Survival Analysis Using S written by Mara Tableman and published by CRC Press. This book was released on 2003-07-28 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: Survival Analysis Using S: Analysis of Time-to-Event Data is designed as a text for a one-semester or one-quarter course in survival analysis for upper-level or graduate students in statistics, biostatistics, and epidemiology. Prerequisites are a standard pre-calculus first course in probability and statistics, and a course in applied linear regression models. No prior knowledge of S or R is assumed. A wide choice of exercises is included, some intended for more advanced students with a first course in mathematical statistics. The authors emphasize parametric log-linear models, while also detailing nonparametric procedures along with model building and data diagnostics. Medical and public health researchers will find the discussion of cut point analysis with bootstrap validation, competing risks and the cumulative incidence estimator, and the analysis of left-truncated and right-censored data invaluable. The bootstrap procedure checks robustness of cut point analysis and determines cut point(s). In a chapter written by Stephen Portnoy, censored regression quantiles - a new nonparametric regression methodology (2003) - is developed to identify important forms of population heterogeneity and to detect departures from traditional Cox models. By generalizing the Kaplan-Meier estimator to regression models for conditional quantiles, this methods provides a valuable complement to traditional Cox proportional hazards approaches.
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 Probability Theory and Extreme Value Theory written by Madan Lal Puri and published by Walter de Gruyter. This book was released on 2011-07-11 with total page 760 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Progressive Censoring written by N. Balakrishnan and published by Springer Science & Business Media. This book was released on 2000-06-16 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new book offers a guide to the theory and methods of progressive censoring. In many industrial experiments involving lifetimes of machines or units, experiments have to be terminated early. Progressive Censoring first introduces progressive sampling foundations, and then discusses various properties of progressive samples. The book points out the greater efficiency gained by using this scheme instead of classical right-censoring methods.
Download or read book Statistical Methods at the Forefront of Biomedical Advances written by Yolanda Larriba and published by Springer Nature. This book was released on 2023-08-09 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents novel statistics methods and reproducible software that helps to solve challenging problems in biomedicine. Specifically, it consists of a collection of 11 chapters contributed by some of the leading experts in the mathematical and statistical field which address new challenges in very disparate biomedical areas, such as genomics, cancer, circadian biology, microbiome, mental disorders, and more. The mathematical rigor is written in a user-friendly way to serve a general biomedical audience ranging from trainees or students to doctors, as well as scientific researchers, university departments, and PhD students.
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 739 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 Statistical Postprocessing of Ensemble Forecasts written by Stéphane Vannitsem and published by Elsevier. This book was released on 2018-05-17 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical Postprocessing of Ensemble Forecasts brings together chapters contributed by international subject-matter experts describing the current state of the art in the statistical postprocessing of ensemble forecasts. The book illustrates the use of these methods in several important applications including weather, hydrological and climate forecasts, and renewable energy forecasting. After an introductory section on ensemble forecasts and prediction systems, the second section of the book is devoted to exposition of the methods available for statistical postprocessing of ensemble forecasts: univariate and multivariate ensemble postprocessing are first reviewed by Wilks (Chapters 3), then Schefzik and Möller (Chapter 4), and the more specialized perspective necessary for postprocessing forecasts for extremes is presented by Friederichs, Wahl, and Buschow (Chapter 5). The second section concludes with a discussion of forecast verification methods devised specifically for evaluation of ensemble forecasts (Chapter 6 by Thorarinsdottir and Schuhen). The third section of this book is devoted to applications of ensemble postprocessing. Practical aspects of ensemble postprocessing are first detailed in Chapter 7 (Hamill), including an extended and illustrative case study. Chapters 8 (Hemri), 9 (Pinson and Messner), and 10 (Van Schaeybroeck and Vannitsem) discuss ensemble postprocessing specifically for hydrological applications, postprocessing in support of renewable energy applications, and postprocessing of long-range forecasts from months to decades. Finally, Chapter 11 (Messner) provides a guide to the ensemble-postprocessing software available in the R programming language, which should greatly help readers implement many of the ideas presented in this book. Edited by three experts with strong and complementary expertise in statistical postprocessing of ensemble forecasts, this book assesses the new and rapidly developing field of ensemble forecast postprocessing as an extension of the use of statistical corrections to traditional deterministic forecasts. Statistical Postprocessing of Ensemble Forecasts is an essential resource for researchers, operational practitioners, and students in weather, seasonal, and climate forecasting, as well as users of such forecasts in fields involving renewable energy, conventional energy, hydrology, environmental engineering, and agriculture. - Consolidates, for the first time, the methodologies and applications of ensemble forecasts in one succinct place - Provides real-world examples of methods used to formulate forecasts - Presents the tools needed to make the best use of multiple model forecasts in a timely and efficient manner
