| Document Type
|
:
|
BL
|
| Record Number
|
:
|
891104
|
| Main Entry
|
:
|
Dörre, Achim
|
| Title & Author
|
:
|
Analysis of doubly truncated data : : an introduction /\ Achim Dörre, Takeshi Emura.
|
| Publication Statement
|
:
|
Singapore :: Springer,, [2019]
|
| Series Statement
|
:
|
SpringerBriefs in Statistics, JSS research series in statistics
|
| Page. NO
|
:
|
1 online resource
|
| ISBN
|
:
|
9789811362415
|
|
|
:
|
: 9811362416
|
|
|
:
|
9789811362408
|
|
|
:
|
9811362408
|
| Bibliographies/Indexes
|
:
|
Includes bibliographical references and index.
|
| Contents
|
:
|
Intro; Preface; Acknowledgements; Contents; Abbreviations; Notations; 1 Introduction to Double-Truncation; 1.1 Doubly Truncated Data; 1.2 Probability Models for Double-Truncation; 1.3 Truncation Bias; 1.4 Likelihood-Based Inference Under Double-Truncation; 1.4.1 Random Double-Truncation; 1.4.2 Fixed-Length Double-Truncation; 1.4.3 Maximum Likelihood Estimation; 1.4.4 Other Estimation Methods; 1.5 Relation to Censoring; References; 2 Parametric Estimation Under Exponential Family; 2.1 Introduction; 2.2 Special Exponential Family (SEF); 2.2.1 One-Parameter Models; 2.2.2 Two-Parameter Models
|
|
|
:
|
2.2.3 Cubic Models2.2.4 More Than Three Parameters; 2.3 Likelihood Function; 2.3.1 One-Parameter Models; 2.3.2 Two-Parameter Models; 2.3.3 Cubic Models; 2.4 The Newton-Raphson Algorithm; 2.4.1 One-Parameter Models; 2.4.2 Two-Parameter Models; 2.4.3 Cubic Models; 2.5 Asymptotic Theory; 2.6 An R Package "double.truncation"; 2.7 Data Analysis; 2.8 Additional Remarks; References; 3 Bayesian Inference for Doubly Truncated Data; 3.1 Introduction; 3.2 Bayesian Inference; 3.3 A Bayesian Model for Double-Truncation; 3.3.1 Birth Process; 3.3.2 Selection Probability
|
|
|
:
|
3.3.3 Homogeneous and Inhomogeneous Birth Processes3.3.4 Density of Observed Lifetimes; 3.3.5 Likelihood Function; 3.3.6 Identifiability; 3.3.7 Exponential Families as a Special Case; 3.4 Estimation; 3.4.1 Metropolis Algorithm; 3.5 Numerical Suggestions; 3.5.1 Numerical Determination of the Selection Probability; 3.5.2 Tuning the Metropolis Algorithm; 3.6 Application; References; 4 Nonparametric Inference for Double-Truncation; 4.1 Introduction; 4.2 Heuristic Derivation of the NPMLE of f; 4.3 Joint Maximum Likelihood Estimate of f and k; 4.4 Asymptotic Properties and Bootstrap Approximation
|
|
|
:
|
4.5 ApplicationReferences; 5 Linear Regression Under Random Double-Truncation; 5.1 Introduction; 5.2 Model and Method; 5.3 Properties of the Estimators; 5.4 Application; References; Appendix A Formula of the SE for the NPMLE; Appendix B Score Function and Hessian Matrix in a Two-Parameter Model; Appendix C R Codes for the Analysis of Childhood Cancer Data; Appendix D R Code for Bayesian Analysis of Doubly Truncated Data; Appendix E R Code for Non-parametric Analysis of Doubly Truncated Data; Appendix F R Code for Linear Regression Under Random Double Truncation; Index
|
| Abstract
|
:
|
This book introduces readers to statistical methodologies used to analyze doubly truncated data. The first book exclusively dedicated to the topic, it provides likelihood-based methods, Bayesian methods, non-parametric methods, and linear regression methods. These procedures can be used to effectively analyze continuous data, especially survival data arising in biostatistics and economics. Because truncation is a phenomenon that is often encountered in non-experimental studies, the methods presented here can be applied to many branches of science. The book provides R codes for most of the statistical methods, to help readers analyze their data. Given its scope, the book is ideally suited as a textbook for students of statistics, mathematics, econometrics, and other fields.
|
| Subject
|
:
|
Mathematical statistics.
|
| Subject
|
:
|
Mathematical statistics.
|
| Dewey Classification
|
:
|
519.5
|
| LC Classification
|
:
|
QA276.D67 2019
|
| Added Entry
|
:
|
Emura, Takeshi
|