Author: Gerhard TutzPublisher:
ISBN:
Category :
Languages : en
Pages : 52
Book Description
Nonparametric Estimation of Discrete Hazard Functions
Author: Gerhard TutzData-Based Nonparametric Estimation of the Hazard Function with Applications to Model Diagnostics and Exploratory Analysis
Author: M. A. TannerModeling Discrete Time-to-Event Data
Author: Gerhard TutzPublisher: Springer
ISBN: 3319281585
Category : Mathematics
Languages : en
Pages : 252
Book Description
This book focuses on statistical methods for the analysis of discrete failure times. Failure time analysis is one of the most important fields in statistical research, with applications affecting a wide range of disciplines, in particular, demography, econometrics, epidemiology and clinical research. Although there are a large variety of statistical methods for failure time analysis, many techniques are designed for failure times that are measured on a continuous scale. In empirical studies, however, failure times are often discrete, either because they have been measured in intervals (e.g., quarterly or yearly) or because they have been rounded or grouped. The book covers well-established methods like life-table analysis and discrete hazard regression models, but also introduces state-of-the art techniques for model evaluation, nonparametric estimation and variable selection. Throughout, the methods are illustrated by real life applications, and relationships to survival analysis in continuous time are explained. Each section includes a set of exercises on the respective topics. Various functions and tools for the analysis of discrete survival data are collected in the R package discSurv that accompanies the book.
Nonparametric Estimation in the Competing Risks Problem
Author: Arthur V. Peterson (Jr.)Publisher:
ISBN:
Category : Estimation theory
Languages : en
Pages : 290
Book Description
Applied Nonparametric Statistics in Reliability
Author: M. Luz GámizPublisher: Springer Science & Business Media
ISBN: 0857291181
Category : Technology & Engineering
Languages : en
Pages : 238
Book Description
Nonparametric statistics has probably become the leading methodology for researchers performing data analysis. It is nevertheless true that, whereas these methods have already proved highly effective in other applied areas of knowledge such as biostatistics or social sciences, nonparametric analyses in reliability currently form an interesting area of study that has not yet been fully explored. Applied Nonparametric Statistics in Reliability is focused on the use of modern statistical methods for the estimation of dependability measures of reliability systems that operate under different conditions. The scope of the book includes: smooth estimation of the reliability function and hazard rate of non-repairable systems; study of stochastic processes for modelling the time evolution of systems when imperfect repairs are performed; nonparametric analysis of discrete and continuous time semi-Markov processes; isotonic regression analysis of the structure function of a reliability system, and lifetime regression analysis. Besides the explanation of the mathematical background, several numerical computations or simulations are presented as illustrative examples. The corresponding computer-based methods have been implemented using R and MATLAB®. A concrete modelling scheme is chosen for each practical situation and, in consequence, a nonparametric inference procedure is conducted. Applied Nonparametric Statistics in Reliability will serve the practical needs of scientists (statisticians and engineers) working on applied reliability subjects.
Functional Estimation For Density, Regression Models And Processes (Second Edition)
Author: Odile PonsPublisher: World Scientific
ISBN: 9811272859
Category : Mathematics
Languages : en
Pages : 259
Book Description
Nonparametric kernel estimators apply to the statistical analysis of independent or dependent sequences of random variables and for samples of continuous or discrete processes. The optimization of these procedures is based on the choice of a bandwidth that minimizes an estimation error and the weak convergence of the estimators is proved. This book introduces new mathematical results on statistical methods for the density and regression functions presented in the mathematical literature and for functions defining more complex models such as the models for the intensity of point processes, for the drift and variance of auto-regressive diffusions and the single-index regression models.This second edition presents minimax properties with Lp risks, for a real p larger than one, and optimal convergence results for new kernel estimators of function defining processes: models for multidimensional variables, periodic intensities, estimators of the distribution functions of censored and truncated variables, estimation in frailty models, estimators for time dependent diffusions, for spatial diffusions and for diffusions with stochastic volatility.
Nonparametric Estimation of Hazard Functions
Author: Samuel Shangwu WuThe Statistical Analysis of Interval-censored Failure Time Data
Author: Jianguo SunPublisher: Springer
ISBN: 0387371192
Category : Mathematics
Languages : en
Pages : 310
Book Description
This book collects and unifies statistical models and methods that have been proposed for analyzing interval-censored failure time data. It provides the first comprehensive coverage of the topic of interval-censored data and complements the books on right-censored data. The focus of the book is on nonparametric and semiparametric inferences, but it also describes parametric and imputation approaches. This book provides an up-to-date reference for people who are conducting research on the analysis of interval-censored failure time data as well as for those who need to analyze interval-censored data to answer substantive questions.
Non-parametric Estimation Under Proportional Hazards Model in Survival Analysis
Author: Rupa Chattopadhyay MitraPublisher:
ISBN:
Category : Estimation theory
Languages : en
Pages : 100
Book Description
Nonparametric Methods for Hazard Rate Estimation from Right-Censored Samples
Author: D. T. McNicholsPublisher:
ISBN:
Category :
Languages : en
Pages : 21
Book Description
Nonparametric estimation of the hazard rate or failure rate is a frequent topic of investigation in the statistical literature because of its practical importance. Until quite recently, hazard rate estimation had been based on complete samples of independent identically distributed lifetimes. However, observations may be censored or truncated in many life testing situations. This occurs often in medical trials when the patients may enter treatment at different times and then either die from the disease under investigation or leave the study before its conclusion. A similar situation may occur in industrial life testing when items are removed from the test at random times for various reasons. It is of interest to be able to estimate nonparametrically the unknown hazard rate of the lifetime random variable from this type of data without ignoring or discarding the right-censored information. The purpose of this paper is to discuss nonparametric estimation of the hazard rate function for right-censored samples. The various types of estimators that have been proposed in the literature will be indicated and briefly discussed in Section 3. These include maximum likelihood estimators, kernel type estimators, Bayesian estimators, and histogram estimators. Due to their computational simplicity and other properties, the kernel-type hazard rate estimators will be emphasized. Results of Tanner (1983) and Tanner and Wong (1983, 1984) will be presented in Section 4 while the estimator considered by McNichols and Padgett (1981) will be discussed in Section 5.