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A Goodness Of Fit Test For Semi Parametric Copula Models For Bivariate Censored Data
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Book Synopsis A Goodness-of-fit Test for Semi-parametric Copula Models for Bivariate Censored Data by : Jimin Shin
Download or read book A Goodness-of-fit Test for Semi-parametric Copula Models for Bivariate Censored Data written by Jimin Shin and published by . This book was released on 2020 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we suggest a goodness-of-fit test for semi-parametric copula models. We extended the pseudo in-and-out-sample (PIOS) test proposed in [17], which is based on the PIOS test in [28]. The PIOS test is constructed by comparing the pseudo "in-sample" likelihood and pseudo "out-of-sample" likelihood. Our contribution is two-fold. First, we use the approximate test statistics instead of the exact test statistics to alleviate the computational burden of calculating the test statistics. Secondly, we propose a parametric bootstrap procedure to approximate the distribution of the test statistic. Unlike the nonparametric bootstrap which resamples from the original data, the parametric procedure resamples the data from the copula model under the null hypothesis. We conduct simulation studies to investigate the performance of the approximate test statistic and parametric bootstrap. The results show that the parametric bootstrap presents higher test power with a well-controlled type I error compared to the nonparametric bootstrap.
Book Synopsis A Goodness-of-fit Test for Semi-parametric Copula Models of Right-censored Bivariate Survival Times by : Moyan Mei
Download or read book A Goodness-of-fit Test for Semi-parametric Copula Models of Right-censored Bivariate Survival Times written by Moyan Mei and published by . This book was released on 2016 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: In multivariate survival analyses, understanding and quantifying the association between survival times is of importance. Copulas, such as Archimedean copulas and Gaussian copulas, provide a flexible approach of modeling and estimating the dependence structure among survival times separately from the marginal distributions (Sklar, 1959). However, misspecification in the parametric form of the copula function will directly lead to incor- rect estimation of the joint distribution of the bivariate survival times and other model-based quantities.The objectives of this project are two-folded. First, I reviewed the basic definitions and properties of commonly used survival copula models. In this project, I focused on semi- parametric copula models where the marginal distributions are unspecified but the copula function belongs to a parametric copula family. Various estimation procedures of the de- pendence parameter associated with the copula function were also reviewed. Secondly, I extended the pseudo in-and-out-of-sample (PIOS) likelihood ratio test proposed in Zhang et al. (2016) to testing the semi-parametric copula models for right-censored bivariate sur- vival times. The PIOS test is constructed by comparing two forms of pseudo likelihoods, one is the "in-sample" pseudo likelihood, which is the full pseudo likelihood, and the other is the "out-of-sample" pseudo likelihood, which is a cross-validated pseudo likelihood by the means of jacknife. The finite sample performance of the PIOS test was investigated via a simulation study. In addition, two real data examples were analyzed for illustrative purpose.
Book Synopsis Estimation and Goodness of Fit for Multivariate Survival Models Based on Copulas by : Yildiz Elif Yilmaz
Download or read book Estimation and Goodness of Fit for Multivariate Survival Models Based on Copulas written by Yildiz Elif Yilmaz and published by . This book was released on 2009 with total page 115 pages. Available in PDF, EPUB and Kindle. Book excerpt: We provide ways to test the fit of a parametric copula family for bivariate censored data with or without covariates. The proposed copula family is tested by embedding it in an expanded parametric family of copulas. When parameters in the proposed and the expanded copula models are estimated by maximum likelihood, a likelihood ratio test can be used. However, when they are estimated by two-stage pseudolikelihood estimation, the corresponding test is a pseudolikelihood ratio test. The two-stage procedures offer less computation, which is especially attractive when the marginal lifetime distributions are specified nonparametrically or semiparametrically. It is shown that the likelihood ratio test is consistent even when the expanded model is misspecified. Power comparisons of the likelihood ratio and the pseudolikelihood ratio tests with some other goodness-of-fit tests are performed both when the expanded family is correct and when it is misspecified. They indicate that model expansion provides a convenient, powerful and robust approach. We introduce a semiparametric maximum likelihood estimation method in which the copula parameter is estimated without assumptions on the marginal distributions. This method and the two-stage semiparametric estimation method suggested by Shih and Louis (1995) are generalized to regression models with Cox proportional hazards margins. The two-stage semiparametric estimator of the copula parameter is found to be about as good as the semiparametric maximum likelihood estimator. Semiparametric likelihood ratio and pseudolikelihood ratio tests are considered to provide goodness of fit tests for a copula model without making parametric assumptions for the marginal distributions. Both when the expanded family is correct and when it is misspecified, the semiparametric pseudolikelihood ratio test is almost as powerful as the parametric likelihood ratio and pseudolikelihood ratio tests while achieving robustness to the form of the marginal distributions. The methods are illustrated on applications in medicine and insurance. Sequentially observed survival times are of interest in many studies but there are difficulties in modeling and analyzing such data. First, when the duration of followup is limited and the times for a given individual are not independent, the problem of induced dependent censoring arises for the second and subsequent survival times. Non-identifiability of the marginal survival distributions for second and later times is another issue, since they are observable only if preceding survival times for an individual are uncensored. In addition, in some studies, a significant proportion of individuals may never have the first event. Fully parametric models can deal with these features, but lack of robustness is a concern, and methods of assessing fit are lacking. We introduce an approach to address these issues. We model the joint distribution of the successive survival times by using copula functions, and provide semiparametric estimation procedures in which copula parameters are estimated without parametric assumptions on the marginal distributions. The performance of semiparametric estimation methods is compared with some other estimation methods in simulation studies and shown to be good. The methodology is applied to a motivating example involving relapse and survival following colon cancer treatment.
Book Synopsis Analysis of Survival Data with Dependent Censoring by : Takeshi Emura
Download or read book Analysis of Survival Data with Dependent Censoring written by Takeshi Emura and published by Springer. This book was released on 2018-04-05 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces readers to copula-based statistical methods for analyzing survival data involving dependent censoring. Primarily focusing on likelihood-based methods performed under copula models, it is the first book solely devoted to the problem of dependent censoring. The book demonstrates the advantages of the copula-based methods in the context of medical research, especially with regard to cancer patients’ survival data. Needless to say, the statistical methods presented here can also be applied to many other branches of science, especially in reliability, where survival analysis plays an important role. The book can be used as a textbook for graduate coursework or a short course aimed at (bio-) statisticians. To deepen readers’ understanding of copula-based approaches, the book provides an accessible introduction to basic survival analysis and explains the mathematical foundations of copula-based survival models.
Book Synopsis The Frailty Model by : Luc Duchateau
Download or read book The Frailty Model written by Luc Duchateau and published by Springer Science & Business Media. This book was released on 2007-10-23 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: Readers will find in the pages of this book a treatment of the statistical analysis of clustered survival data. Such data are encountered in many scientific disciplines including human and veterinary medicine, biology, epidemiology, public health and demography. A typical example is the time to death in cancer patients, with patients clustered in hospitals. Frailty models provide a powerful tool to analyze clustered survival data. In this book different methods based on the frailty model are described and it is demonstrated how they can be used to analyze clustered survival data. All programs used for these examples are available on the Springer website.
Book Synopsis Statistical Analysis of Bivariate Interval-censored Failure Time Data by : Qingning Zhou
Download or read book Statistical Analysis of Bivariate Interval-censored Failure Time Data written by Qingning Zhou and published by . This book was released on 2015 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation deals with various issues in the statistical analysis of bivariate interval-censored failure time data, including regression analysis, model selection and estimation of the association between failure times. In particular, it includes three projects. The first project discusses regression analysis of bivariate current status data under the marginal proportional hazards model. For the problem, by using Bernstein polynomials and an unspecified copula model, we develop a sieve maximum likelihood estimation approach that applies to very general situations. In particular, it allows one to estimate the underlying copula model and can be easily implemented. The strong consistency, asymptotic normality and efficiency of the estimators of regression parameters are established. In the second project, we consider regression analysis of bivariate case II interval-censored data. For this problem, we present a class of semiparametric transformation models which is very flexible and in particular includes the commonly used proportional hazards model as a special case. Also, for inference, we develop a sieve maximum likelihood approach based on Bernstein polynomials. The strong consistency, asymptotic normality and efficiency of the resulting estimators of the regression parameters are established. In the third project, we consider the class of semiparametric copula-based models, in which multivariate survival functions are characterized by parametric copulas and nonparametric marginal survival functions. One important issue in applying this class of models to a given data set is how to choose an appropriate parametric copula. We propose two model selection procedures for Archimedean copulas with bivariate interval-censored data. The first procedure is based on a comparison of the nonparametric and model-based estimators of the probability integral transformation K, while the second procedure is based on a pseudo-likelihood function.
Book Synopsis Emerging Topics in Modeling Interval-Censored Survival Data by : Jianguo Sun
Download or read book Emerging Topics in Modeling Interval-Censored Survival Data written by Jianguo Sun and published by Springer Nature. This book was released on 2022-11-29 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book primarily aims to discuss emerging topics in statistical methods and to booster research, education, and training to advance statistical modeling on interval-censored survival data. Commonly collected from public health and biomedical research, among other sources, interval-censored survival data can easily be mistaken for typical right-censored survival data, which can result in erroneous statistical inference due to the complexity of this type of data. The book invites a group of internationally leading researchers to systematically discuss and explore the historical development of the associated methods and their computational implementations, as well as emerging topics related to interval-censored data. It covers a variety of topics, including univariate interval-censored data, multivariate interval-censored data, clustered interval-censored data, competing risk interval-censored data, data with interval-censored covariates, interval-censored data from electric medical records, and misclassified interval-censored data. Researchers, students, and practitioners can directly make use of the state-of-the-art methods covered in the book to tackle their problems in research, education, training and consultation.
Book Synopsis Testing the Goodness of Fit of a Copula Based on Bivariate Right Censored Data by : Per Kragh Andersen
Download or read book Testing the Goodness of Fit of a Copula Based on Bivariate Right Censored Data written by Per Kragh Andersen and published by . This book was released on 2001 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Nonparametric Tests for Censored Data by : Vilijandas Bagdonavicius
Download or read book Nonparametric Tests for Censored Data written by Vilijandas Bagdonavicius and published by John Wiley & Sons. This book was released on 2013-02-07 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book concerns testing hypotheses in non-parametric models. Generalizations of many non-parametric tests to the case of censored and truncated data are considered. Most of the test results are proved and real applications are illustrated using examples. Theories and exercises are provided. The incorrect use of many tests applying most statistical software is highlighted and discussed.
Book Synopsis Copulae in Mathematical and Quantitative Finance by : Piotr Jaworski
Download or read book Copulae in Mathematical and Quantitative Finance written by Piotr Jaworski and published by Springer Science & Business Media. This book was released on 2013-06-18 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: Copulas are mathematical objects that fully capture the dependence structure among random variables and hence offer great flexibility in building multivariate stochastic models. Since their introduction in the early 1950s, copulas have gained considerable popularity in several fields of applied mathematics, especially finance and insurance. Today, copulas represent a well-recognized tool for market and credit models, aggregation of risks, and portfolio selection. Historically, the Gaussian copula model has been one of the most common models in credit risk. However, the recent financial crisis has underlined its limitations and drawbacks. In fact, despite their simplicity, Gaussian copula models severely underestimate the risk of the occurrence of joint extreme events. Recent theoretical investigations have put new tools for detecting and estimating dependence and risk (like tail dependence, time-varying models, etc) in the spotlight. All such investigations need to be further developed and promoted, a goal this book pursues. The book includes surveys that provide an up-to-date account of essential aspects of copula models in quantitative finance, as well as the extended versions of talks selected from papers presented at the workshop in Cracow.
Book Synopsis Multivariate Models and Multivariate Dependence Concepts by : Harry Joe
Download or read book Multivariate Models and Multivariate Dependence Concepts written by Harry Joe and published by CRC Press. This book was released on 1997-05-01 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book on multivariate models, statistical inference, and data analysis contains deep coverage of multivariate non-normal distributions for modeling of binary, count, ordinal, and extreme value response data. It is virtually self-contained, and includes many exercises and unsolved problems.
Book Synopsis On Some Goodness-Of-Fit Tests for Copulas by : Wei Lu
Download or read book On Some Goodness-Of-Fit Tests for Copulas written by Wei Lu and published by Open Dissertation Press. This book was released on 2017-01-26 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation, "On Some Goodness-of-fit Tests for Copulas" by Wei, Lu, 吕薇, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Copulas have been known in the statistical literature for many years, and have become useful tools in modeling dependence structure of multivariate random variables, overcoming some of the drawbacks of the commonly-used correlation measures. Goodness-of-fit tests for copulas play a very important role in evaluating the suitability of a potential input copula model. In recent years, many approaches have been proposed for constructing goodness-of-fit tests for copula families. Among them, the so-called "blanket tests" do not require an arbitrary data categorization or any strategic choice of weight function, smoothing parameter, kernel, and so on. As preliminaries, some background and related results of copulas are firstly presented. Three goodness-of-fit test statistics belonging to the blanket test classification are then introduced. Since the asymptotic distributions of the test statistics are very complicated, parametric bootstrap procedures are employed to approximate critical values of the test statistics under the null hypotheses. To assess the performance of the three test statistics in the low dependence cases, simulation studies are carried out for three bivariate copula families, namely the Gumbel-Hougaard copula family, the Ali-Mikhail-Haq copula family, and the Farlie-Gumbel-Morgenstern copula family. Specifically the effect of low dependence on the empirical sizes and powers of the three blanket tests under various combinations of null and alternative copula families are examined. Furthermore, to check the performance of the three tests for higher dimensional copulas, the simulation studies are extended to some three-dimensional copulas. Finally the three goodness-of-fit tests are applied to two real data sets. DOI: 10.5353/th_b4784996 Subjects: Copulas (Mathematical statistics) Goodness-of-fit tests
Book Synopsis Elements of Copula Modeling with R by : Marius Hofert
Download or read book Elements of Copula Modeling with R written by Marius Hofert and published by Springer. This book was released on 2019-01-09 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the main theoretical findings related to copulas and shows how statistical modeling of multivariate continuous distributions using copulas can be carried out in the R statistical environment with the package copula (among others). Copulas are multivariate distribution functions with standard uniform univariate margins. They are increasingly applied to modeling dependence among random variables in fields such as risk management, actuarial science, insurance, finance, engineering, hydrology, climatology, and meteorology, to name a few. In the spirit of the Use R! series, each chapter combines key theoretical definitions or results with illustrations in R. Aimed at statisticians, actuaries, risk managers, engineers and environmental scientists wanting to learn about the theory and practice of copula modeling using R without an overwhelming amount of mathematics, the book can also be used for teaching a course on copula modeling.
Book Synopsis Chi-squared Goodness-of-fit Tests for Censored Data by : Mikhail S. Nikulin
Download or read book Chi-squared Goodness-of-fit Tests for Censored Data written by Mikhail S. Nikulin and published by John Wiley & Sons. This book was released on 2017-07-06 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the problems of construction and application of chi-squared goodness-of-fit tests for complete and censored data. Classical chi-squared tests assume that unknown distribution parameters are estimated using grouped data, but in practice this assumption is often forgotten. In this book, we consider modified chi-squared tests, which do not suffer from such a drawback. The authors provide examples of chi-squared tests for various distributions widely used in practice, and also consider chi-squared tests for the parametric proportional hazards model and accelerated failure time model, which are widely used in reliability and survival analysis. Particular attention is paid to the choice of grouping intervals and simulations. This book covers recent innovations in the field as well as important results previously only published in Russian. Chi-squared tests are compared with other goodness-of-fit tests (such as the Cramer-von Mises-Smirnov, Anderson-Darling and Zhang tests) in terms of power when testing close competing hypotheses.
Book Synopsis On Goodness-of-fit Tests of Semiparametric Models by : Bo Li
Download or read book On Goodness-of-fit Tests of Semiparametric Models written by Bo Li and published by . This book was released on 2006 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Seminar on Empirical Processes by : P. Gaenssler
Download or read book Seminar on Empirical Processes written by P. Gaenssler and published by Birkhäuser. This book was released on 2013-11-21 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Survival Analysis with Correlated Endpoints by : Takeshi Emura
Download or read book Survival Analysis with Correlated Endpoints written by Takeshi Emura and published by Springer. This book was released on 2019-03-25 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces readers to advanced statistical methods for analyzing survival data involving correlated endpoints. In particular, it describes statistical methods for applying Cox regression to two correlated endpoints by accounting for dependence between the endpoints with the aid of copulas. The practical advantages of employing copula-based models in medical research are explained on the basis of case studies. In addition, the book focuses on clustered survival data, especially data arising from meta-analysis and multicenter analysis. Consequently, the statistical approaches presented here employ a frailty term for heterogeneity modeling. This brings the joint frailty-copula model, which incorporates a frailty term and a copula, into a statistical model. The book also discusses advanced techniques for dealing with high-dimensional gene expressions and developing personalized dynamic prediction tools under the joint frailty-copula model. To help readers apply the statistical methods to real-world data, the book provides case studies using the authors’ original R software package (freely available in CRAN). The emphasis is on clinical survival data, involving time-to-tumor progression and overall survival, collected on cancer patients. Hence, the book offers an essential reference guide for medical statisticians and provides researchers with advanced, innovative statistical tools. The book also provides a concise introduction to basic multivariate survival models.
