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Author : Gunky Kim
Publisher :
ISBN 13 :
Total Pages : 566 pages
Book Rating : 4.:/5 (752 download)
Download or read book Semiparametric Estimation of Copula Parameters written by Gunky Kim and published by . This book was released on 2008 with total page 566 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Shigeyuki Hamori
Publisher :
ISBN 13 :
Total Pages : 51 pages
Book Rating : 4.:/5 (13 download)
Download or read book Calibration Estimation of Semiparametric Copula Models with Data Missing at Random written by Shigeyuki Hamori and published by . This book was released on 2018 with total page 51 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper investigates the estimation of semiparametric copula models with data missing at random. The two-step maximum likelihood estimation of Genest, Ghoudi, and Rivest (1995) is infeasible if there are missing data. We propose a class of calibration estimators for the nonparametric marginal distributions and the copula parameters of interest by balancing the empirical moments of covariates between observed and whole groups. Our proposed estimators do not require the estimation of missing mechanism, and enjoy stable performance even when sample size is small. We prove that our estimators satisfy consistency and asymptotic normality. We also provide a consistent estimator for the asymptotic variance. We show via extensive simulations that our proposed method dominates existing alternatives.
Author : Yildiz Elif Yilmaz
Publisher :
ISBN 13 :
Total Pages : 115 pages
Book Rating : 4.:/5 (926 download)
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.
Author : Sawitree Boonpatcharanon
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (136 download)
Download or read book Semiparametric Multivariate Density Estimation Using Copulas and Shape-Constraints written by Sawitree Boonpatcharanon and published by . This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Maximum likelihood estimation of a log-concave density has certain advantages over other nonparametric approaches, such as kernel density estimation, which requires a bandwidth selection. Furthermore, finding the optimal bandwidth gets more difficult as a dimension increases. On the other hand, the shape-constrained approach is automatic and does not need any tuning parameters. However, for both the kernel and log-concave estimators, the rate of convergence slows down as the dimension d increases. To handle this "curse of dimensionality", we study an intermediate semi-parametric copula approach and we estimate the marginals using the log-concave shape-constrained MLE and use a parametric approach to fit the copula parameters. We prove square root n rate of convergence for the parametric estimator and that the joint density converges at a rate of n^(-2/5) regardless of dimension. This is faster than the conjectured rate of n^(-2/(d+4)) for the multivariate log-concave estimators. We examine the performance of our proposed method via simulation studies and real data example.
Author : Johan Segers
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)
Download or read book Semiparametric Gaussian Copula Models written by Johan Segers and published by . This book was released on 2013 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: For multivariate Gaussian copula models with unknown margins and structured correlation matrices, a rank-based, semiparametrically effi cient estimator is proposed for the Euclidean copula parameter. This estimator is defined as a one-step update of a rank-based pilot estimator in the direction of the e fficient influence function, which is calculated explicitly. Moreover, finite-dimensional algebraic conditions are given that completely characterize adaptivity of the model with respect to the unknown marginal distributions and of efficiency of the pseudo-likelihood estimator. For correlation matrices structured according to a factor model, the pseudo-likelihood estimator turns out to be semiparametrically effi cient. On the other hand, for Toeplitz correlation matrices, the asymptotic relative effi ciency of the pseudo-likelihood estimator with respect to our one-step estimator can be as low as 20%. These findings are confirmed by Monte Carlo simulations.
Author : Byungsoo Kim
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)
Download or read book Robust Estimation for Copula Parameter in SCOMDY Models written by Byungsoo Kim and published by . This book was released on 2013 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this study, we study the robust estimation for the copula parameter in semiparametric copula-based multivariate dynamic (SCOMDY) models proposed by Chen and Fan (2006). To this end, instead of the pseudo maximum likelihood estimator in Chen and Fan (2006), we use a minimum density power divergence estimator (MDPDE) proposed by Basu et al. (1998). It is shown that the MDPDE is consistent and asymptotically normal under regularity conditions. We compare the performance between the two estimators when outliers exist through a simulation study.
Author : Xiaohong Chen
Publisher :
ISBN 13 :
Total Pages : 56 pages
Book Rating : 4.:/5 (129 download)
Download or read book Efficient Estimation of Copula-Based Semiparametric Markov Models written by Xiaohong Chen and published by . This book was released on 2009 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper considers efficient estimation of copula-based semiparametric strictly stationary Markov models. These models are characterized by nonparametric invariant (one-dimensional marginal) distributions and parametric bivariate copula functions; where the copulas capture temporal dependence and tail dependence of the processes. The Markov processes generated via tail dependent copulas may look highly persistent and are useful for financial and economic applications. We first show that Markov processes generated via Clayton, Gumbel and Student's $t$ copulas and their survival copulas are all geometrically ergodic. We then propose a sieve maximum likelihood estimation (MLE) for the copula parameter, the invariant distribution and the conditional quantiles. We show that the sieve MLEs of any smooth functionals are root-$n$ consistent, asymptotically normal and efficient; and that their sieve likelihood ratio statistics are asymptotically chi-square distributed. We present Monte Carlo studies to compare the finite sample performance of the sieve MLE, the two-step estimator of Chen and Fan (2006), the correctly specified parametric MLE and the incorrectly specified parametric MLE. The simulation results indicate that our sieve MLEs perform very well; having much smaller biases and smaller variances than the two-step estimator for Markov models generated via Clayton, Gumbel and other tail dependent copulas.
Author : Piotr Jaworski
Publisher : Springer Science & Business Media
ISBN 13 : 3642124658
Total Pages : 338 pages
Book Rating : 4.6/5 (421 download)
Download or read book Copula Theory and Its Applications written by Piotr Jaworski and published by Springer Science & Business Media. This book was released on 2010-07-16 with total page 338 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 50's, copulas have gained considerable popularity in several fields of applied mathematics, such as finance, insurance and reliability theory. Today, they represent a well-recognized tool for market and credit models, aggregation of risks, portfolio selection, etc. This book is divided into two main parts: Part I - "Surveys" contains 11 chapters that provide an up-to-date account of essential aspects of copula models. Part II - "Contributions" collects the extended versions of 6 talks selected from papers presented at the workshop in Warsaw.
Author : Arkady Shemyakin
Publisher : John Wiley & Sons
ISBN 13 : 1118959035
Total Pages : 350 pages
Book Rating : 4.1/5 (189 download)
Download or read book Introduction to Bayesian Estimation and Copula Models of Dependence written by Arkady Shemyakin and published by John Wiley & Sons. This book was released on 2017-02-24 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents an introduction to Bayesian statistics, presents an emphasis on Bayesian methods (prior and posterior), Bayes estimation, prediction, MCMC,Bayesian regression, and Bayesian analysis of statistical modelsof dependence, and features a focus on copulas for risk management Introduction to Bayesian Estimation and Copula Models of Dependence emphasizes the applications of Bayesian analysis to copula modeling and equips readers with the tools needed to implement the procedures of Bayesian estimation in copula models of dependence. This book is structured in two parts: the first four chapters serve as a general introduction to Bayesian statistics with a clear emphasis on parametric estimation and the following four chapters stress statistical models of dependence with a focus of copulas. A review of the main concepts is discussed along with the basics of Bayesian statistics including prior information and experimental data, prior and posterior distributions, with an emphasis on Bayesian parametric estimation. The basic mathematical background of both Markov chains and Monte Carlo integration and simulation is also provided. The authors discuss statistical models of dependence with a focus on copulas and present a brief survey of pre-copula dependence models. The main definitions and notations of copula models are summarized followed by discussions of real-world cases that address particular risk management problems. In addition, this book includes: • Practical examples of copulas in use including within the Basel Accord II documents that regulate the world banking system as well as examples of Bayesian methods within current FDA recommendations • Step-by-step procedures of multivariate data analysis and copula modeling, allowing readers to gain insight for their own applied research and studies • Separate reference lists within each chapter and end-of-the-chapter exercises within Chapters 2 through 8 • A companion website containing appendices: data files and demo files in Microsoft® Office Excel®, basic code in R, and selected exercise solutions Introduction to Bayesian Estimation and Copula Models of Dependence is a reference and resource for statisticians who need to learn formal Bayesian analysis as well as professionals within analytical and risk management departments of banks and insurance companies who are involved in quantitative analysis and forecasting. This book can also be used as a textbook for upper-undergraduate and graduate-level courses in Bayesian statistics and analysis. ARKADY SHEMYAKIN, PhD, is Professor in the Department of Mathematics and Director of the Statistics Program at the University of St. Thomas. A member of the American Statistical Association and the International Society for Bayesian Analysis, Dr. Shemyakin's research interests include informationtheory, Bayesian methods of parametric estimation, and copula models in actuarial mathematics, finance, and engineering. ALEXANDER KNIAZEV, PhD, is Associate Professor and Head of the Department of Mathematics at Astrakhan State University in Russia. Dr. Kniazev's research interests include representation theory of Lie algebras and finite groups, mathematical statistics, econometrics, and financial mathematics.
Author : Geert Molenberghs
Publisher : John Wiley & Sons
ISBN 13 : 9780470510438
Total Pages : 526 pages
Book Rating : 4.5/5 (14 download)
Download or read book Missing Data in Clinical Studies written by Geert Molenberghs and published by John Wiley & Sons. This book was released on 2007-04-04 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: Missing Data in Clinical Studies provides a comprehensive account of the problems arising when data from clinical and related studies are incomplete, and presents the reader with approaches to effectively address them. The text provides a critique of conventional and simple methods before moving on to discuss more advanced approaches. The authors focus on practical and modeling concepts, providing an extensive set of case studies to illustrate the problems described. Provides a practical guide to the analysis of clinical trials and related studies with missing data. Examines the problems caused by missing data, enabling a complete understanding of how to overcome them. Presents conventional, simple methods to tackle these problems, before addressing more advanced approaches, including sensitivity analysis, and the MAR missingness mechanism. Illustrated throughout with real-life case studies and worked examples from clinical trials. Details the use and implementation of the necessary statistical software, primarily SAS. Missing Data in Clinical Studies has been developed through a series of courses and lectures. Its practical approach will appeal to applied statisticians and biomedical researchers, in particular those in the biopharmaceutical industry, medical and public health organisations. Graduate students of biostatistics will also find much of benefit.
Author : Harry Joe
Publisher : World Scientific
ISBN 13 : 981429988X
Total Pages : 370 pages
Book Rating : 4.8/5 (142 download)
Download or read book Dependence Modeling written by Harry Joe and published by World Scientific. This book was released on 2011 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. Introduction : Dependence modeling / D. Kurowicka -- 2. Multivariate copulae / M. Fischer -- 3. Vines arise / R.M. Cooke, H. Joe and K. Aas -- 4. Sampling count variables with specified Pearson correlation : A comparison between a naive and a C-vine sampling approach / V. Erhardt and C. Czado -- 5. Micro correlations and tail dependence / R.M. Cooke, C. Kousky and H. Joe -- 6. The Copula information criterion and Its implications for the maximum pseudo-likelihood estimator / S. Gronneberg -- 7. Dependence comparisons of vine copulae with four or more variables / H. Joe -- 8. Tail dependence in vine copulae / H. Joe -- 9. Counting vines / O. Morales-Napoles -- 10. Regular vines : Generation algorithm and number of equivalence classes / H. Joe, R.M. Cooke and D. Kurowicka -- 11. Optimal truncation of vines / D. Kurowicka -- 12. Bayesian inference for D-vines : Estimation and model selection / C. Czado and A. Min -- 13. Analysis of Australian electricity loads using joint Bayesian inference of D-vines with autoregressive margins / C. Czado, F. Gartner and A. Min -- 14. Non-parametric Bayesian belief nets versus vines / A. Hanea -- 15. Modeling dependence between financial returns using pair-copula constructions / K. Aas and D. Berg -- 16. Dynamic D-vine model / A. Heinen and A. Valdesogo -- 17. Summary and future directions / D. Kurowicka
Author : P. Gaenssler
Publisher : Birkhäuser
ISBN 13 : 3034862695
Total Pages : 117 pages
Book Rating : 4.0/5 (348 download)
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:
Author : Lan Zhang
Publisher : Cambridge University Press
ISBN 13 : 110847425X
Total Pages : 621 pages
Book Rating : 4.1/5 (84 download)
Download or read book Copulas and Their Applications in Water Resources Engineering written by Lan Zhang and published by Cambridge University Press. This book was released on 2019-01-10 with total page 621 pages. Available in PDF, EPUB and Kindle. Book excerpt: Illustration of copula theory with detailed real-world case study examples in the fields of hydrology and water resources engineering.
Author : Moyan Mei
Publisher :
ISBN 13 :
Total Pages : 36 pages
Book Rating : 4.:/5 (112 download)
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.
Author : Xiaohong Chen
Publisher :
ISBN 13 :
Total Pages : 39 pages
Book Rating : 4.:/5 (129 download)
Download or read book Estimation and Model Selection of Semiparametric Multivariate Survival Functions under General Censorship written by Xiaohong Chen and published by . This book was released on 2008 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many models of semiparametric multivariate survival functions are characterized by nonparametric marginal survival functions and parametric copula functions, where different copulas imply different dependence structures. This paper considers estimation and model selection for these semiparametric multivariate survival functions, allowing for misspecified parametric copulas and data subject to general censoring. We first establish convergence of the two-step estimator of the copula parameter to the pseudo-true value defined as the value of the parameter that minimizes the KLIC between the parametric copula induced multivariate density and the unknown true density. We then derive its root-n asymptotically normal distribution and provide a simple consistent asymptotic variance estimator by accounting for the impact of the nonparametric estimation of the marginal survival functions. These results are used to establish the asymptotic distribution of the penalized pseudo-likelihood ratio statistic for comparing multiple semiparametric multivariate survival functions subject to copula misspecification and general censorship. An empirical application of the model selection test to the Loss-ALAE insurance data set is provided.
Author : Dean Fantazzini
Publisher :
ISBN 13 :
Total Pages : 50 pages
Book Rating : 4.:/5 (129 download)
Download or read book Three-Stage Semi-Parametric Estimation of T-Copulas written by Dean Fantazzini and published by . This book was released on 2011 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt: Genest, C., Ghoudi, K., Rivest, L.P. (1995) proposed a two-stage semi-parametric estimation procedure for a broad class of copulas satisfying minimal regularity conditions. A three-stage semi-parametric estimation method based on Kendall's tau has been recently proposed in the financial literature to estimate the Student's T copula, too. Its major advantage is to allow for greater computational tractability when dealing with high dimensional issues, where two-stage procedures are no more a viable choice. The asymptotic properties of this methodology are developed and its finite-sample behavior are examined via simulations. The pros and cons of this methodology are then analyzed in terms of numerical convergence and positive definiteness of the estimated T-copula correlation matrix.
Author : Harry Joe
Publisher : CRC Press
ISBN 13 : 9780412073311
Total Pages : 422 pages
Book Rating : 4.0/5 (733 download)
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.
