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Empirical Likelihood Methods in Biomedicine and Health [Kõva köide]

(The State University of New York, Buffalo, USA), (The State University of New York, Buffalo, USA)
  • Formaat: Hardback, 300 pages, kõrgus x laius: 234x156 mm, kaal: 606 g, 18 Tables, black and white; 12 Line drawings, black and white; 12 Illustrations, black and white
  • Ilmumisaeg: 22-Aug-2018
  • Kirjastus: CRC Press Inc
  • ISBN-10: 1466555033
  • ISBN-13: 9781466555037
Teised raamatud teemal:
Empirical Likelihood Methods in Biomedicine and HealthSuurem pilt
  • Formaat: Hardback, 300 pages, kõrgus x laius: 234x156 mm, kaal: 606 g, 18 Tables, black and white; 12 Line drawings, black and white; 12 Illustrations, black and white
  • Ilmumisaeg: 22-Aug-2018
  • Kirjastus: CRC Press Inc
  • ISBN-10: 1466555033
  • ISBN-13: 9781466555037
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781466555037.html
Märksõnad:
Empirical Likelihood Methods in Biomedicine and Health provides a compendium of nonparametric likelihood statistical techniques in the perspective of health research applications. It includes detailed descriptions of the theoretical underpinnings of recently developed empirical likelihood-based methods. The emphasis throughout is on the application of the methods to the health sciences, with worked examples using real data.





Provides a systematic overview of novel empirical likelihood techniques. Presents a good balance of theory, methods, and applications. Features detailed worked examples to illustrate the application of the methods. Includes R code for implementation.

The book material is attractive and easily understandable to scientists who are new to the research area and may attract statisticians interested in learning more about advanced nonparametric topics including various modern empirical likelihood methods. The book can be used by graduate students majoring in biostatistics, or in a related field, particularly for those who are interested in nonparametric methods with direct applications in Biomedicine.

Arvustused

"As far as I know, Empirical Likelihood Methods in Biomedicine and Health is the first book that provides a compendium of nonparametric likelihood statistical techniques in the perspective of health research applications. It focuses on the application of the methods to health sciences, with worked examples using real data. The book is well written. It is comprehensive and informative. The book material is attractive and easily understandable to scientists who are new to the research area and may attract statisticians interested in learning more about advanced nonparametric topics, including various modern empirical likelihood methods. The book contains interesting examples and plenty of R codes. These features make the book suitable as a self-learning text for applied statisticians. The book can also be used by graduate students majoring in biostatistics or in a related field, particularly for those who are interested in nonparametric methods with direct applications in biomedicine." Gengsheng Qin, Department of Mathematics and Statistics, Georgia State University, Atlanta, Georgia, in Statistics in Medicine, January 2019

"This textbook discusses some of the classical statistical problems in the fields of biomedicine and health within the framework of empirical likelihood methodology as introduced and further explained by Owen (1988, 2001)... In an overall assessment, the book provides methodological and computational details for a wide range of problems found in biostatistics. This book is accessible to a wide audience (medical statisticians, researchers in public health, and others) and can serve as a textbook for a graduate special topics class ... The text is well structured. The methods are discussed from the point of view of both theory and applications. The authors have done a great job including R code to illustrate the theory. Furthermore, several data examples are used to motivate discussion of various modeling issues and to provide insight into the nature of the data that arise in this field. I greatly enjoyed reading the book, and I believe that it will serve as a valuable reference for anyone who wishes to study modern methods of inference in biomedicine and health." - Konstantinos Fokianos, Lancaster University

Preface xiii
Authors xvii
1 Preliminaries
1(18)
1.1 Overview: From Statistical Hypotheses to Types of Information for Constructing Statistical Tests
1(1)
1.2 Parametric Approach
2(1)
1.3 Warning---Parametric Approach and Detour: Nonparametric Approach
3(1)
1.4 A Brief Ode to Likelihood
4(4)
1.4.1 Likelihood Ratios and Optimality
6(1)
1.4.2 The Likelihood Ratio Based on the Likelihood Ratio Test Statistic Is the Likelihood Ratio Test Statistic
7(1)
1.5 Maximum Likelihood: Is It the Likelihood?
8(2)
1.5 Empirical Likelihood
10(2)
1.7 Why Empirical Likelihood?
12(7)
1.7.1 The Necessity and Danger of Testing Statistical Hypothesis
12(1)
1.7.2 The Three Sources That Support the Empirical Likelihood Methodology for Applying in Practice
13(1)
Appendix
14(5)
2 Basic Ingredients of the Empirical Likelihood
19(40)
2.1 Introduction
19(1)
2.2 Classical Empirical Likelihood Methods
20(2)
2.3 Techniques for Analyzing Empirical Likelihoods
22(5)
2.3.1 Illustrative Comparison of Empirical Likelihood and Parametric Likelihood
23(4)
2.4 In Case of the Presence of Extra Estimating Equation Information
27(3)
2.4.1 Sketch of the Proof of Equation (2.9)
28(2)
2.5 Some Helpful Properties
30(4)
2.6 Density-Based Empirical Likelihood Methods
34(4)
2.7 Flexible Likelihood Approach Using Empirical Likelihood
38(2)
2.8 Bayesians and Empirical Likelihood: Are They Mutually Exclusive?
40(3)
2.8.1 Nonparametric Posterior Expectations of Simple Functionals
42(1)
2.9 Bartlett Correction
43(1)
2.10 Empirical Likelihood in a Class of Empirical Goodness of Fit Tests
44(2)
2.11 Empirical Likelihood as a Competitor of the Bootstrap
46(2)
2.13 Convex Hull
48(1)
2.14 Empirical Likelihood with Plug-In Estimators
49(1)
2.15 Implementation of Empirical Likelihood Using R
50(9)
Appendix
52(7)
3 Empirical Likelihood in Light of Nonparametric Bayesian Inference
59(50)
3.1 Introduction
59(1)
3.2 Posterior Expectation Incorporating Empirical Likelihood
60(11)
3.2.1 Nonparametric Posterior Expectations of Simple Functionals
62(5)
3.2.2 Nonparametric Posterior Expectations of General Functionals
67(2)
3.2.3 Nonparametric Analog of James-Stein Estimation
69(1)
3.2.4 Performance of the Empirical Likelihood Bayesian Estimators
70(1)
3.3 Confidence Interval Estimation with Adjustment for Skewed Data
71(9)
3.3.1 Data-Driven Equal-Tailed CI Estimation
72(3)
3.3.2 Data-Driven Highest Posterior Density CI Estimation
75(2)
3.3.3 General Cases for CI Estimation
77(2)
3.3.4 Performance of the Empirical Likelihood Bayesian CIs
79(1)
3.3.5 Strategy to Analyze Real Data
79(1)
3.4 Some Warnings
80(2)
3.5 An Example of the Use of Empirical Likelihood-Based Bayes Factors in the Bayesian Manner
82(4)
3.6 Concluding Remarks
86(23)
Appendix
86(23)
4 Empirical Likelihood for Probability Weighted Moments
109(28)
4.1 Introduction
109(1)
4.2 Incorporating the Empirical Likelihood for βr
110(7)
4.2.1 Estimators of the Probability Weighted Moments
110(2)
4.2.2 Empirical Likelihood Inference for βr
112(2)
4.2.3 A Scheme to Implement the Empirical Likelihood Ratio Technique
114(1)
4.2.4 An Application to the Gini Index
115(2)
4.3 Performance Comparisons
117(3)
4.4 Data Example
120(1)
4.5 Concluding Remarks
121(16)
Appendix
121(16)
5 Two-Group Comparison and Combining Likelihoods Based on Incomplete Data
137(26)
5.1 Introduction
137(1)
5.2 Product of Likelihood Functions Based on the Empirical Likelihood
138(2)
5.3 Classical Empirical Likelihood Tests to Compare Means
140(6)
5.3.1 Implementation in R
143(2)
5.3.2 Implementation Using Available R Packages
145(1)
5.4 Classical Empirical Likelihood Ratio Tests to Compare Multivariate Means
146(3)
5.4.1 Profile Analysis
147(2)
5.5 Product of Likelihood Functions Based on the Empirical Likelihood
149(6)
5.5.1 Product of Empirical Likelihood and Parametric Likelihood
149(1)
5.5.1.1 Implementation in R
150(2)
5.5.2 Product of the Empirical Likelihoods
152(2)
5.5.2.1 Implementation in R (Continued from Section 5.5.1.1)
154(1)
5.6 Concluding Remarks
155(8)
Appendix
155(8)
6 Quantile Comparisons
163(24)
6.1 Introduction
163(3)
6.2 Existing Nonparametric Tests to Compare Location Shifts
166(1)
6.3 Empirical Likelihood Tests to Compare Location Shifts
167(8)
6.3.1 Plug-in Approach
171(4)
6.4 Computation in R
175(5)
6.5 Constructing Confidence Intervals on Quantile Differences
180(4)
6.6 Concluding Remarks
184(3)
Appendix
184(3)
7 Empirical Likelihood for a U-Statistic Constraint
187(32)
7.1 Introduction
187(1)
7.2 Empirical Likelihood Statistic for a U-Statistics Constraint
188(5)
7.3 Two-Sample Setting
193(4)
7.4 Various Applications
197(13)
7.4.1 Receiver Operating Characteristic Curve Analysis
197(1)
7.4.1.1 R Code
198(3)
7.4.2 Generalization for Comparing Two Correlated AUC Statistics
201(1)
7.4.2.1 Implementation in R
202(2)
7.4.3 Comparison of Two Survival Curves
204(1)
7.4.3.1 R Code
205(1)
7.4.4 Multivariate Rank-Based Tests
206(1)
7.4.4.1 AAA Implementation in R
207(2)
7.4.4.2 Comments on the Performance of the Empirical Likelihood Ratio Statistics
209(1)
7.5 An Application to Crossover Designs
210(4)
7.5 Concluding Remarks
214(5)
Appendix
214(5)
8 Empirical Likelihood Application to Receiver Operating Characteristic Curve Analysis
219(28)
8.1 Introduction
219(1)
8.2 Receiver Operating Characteristic Curve
220(2)
8.3 Area under the Receiver Operating Characteristic Curve
222(1)
8.4 Nonparametric Comparison of Two Receiver Operating Characteristic Curves
223(1)
8.5 Best Combinations Based on Values of Multiple Biomarkers
224(4)
8.6 Partial Area under the Receiver Operating Characteristic Curve
228(14)
8.6.1 Alternative Expression of the pAUC Estimator for the Variance Estimation
229(4)
8.6.2 Comparison of Two Correlated pAUC Estimates
233(1)
8.6.3 An Empirical Likelihood Approach Based on the Proposed Variance Estimator
234(8)
8.7 Concluding Remarks
242(5)
Appendix
243(4)
9 Various Topics
247(30)
9.1 Introduction
247(1)
9.2 Various Regression Approaches
247(10)
9.2.1 General Framework
247(4)
9.2.2 Analyzing Longitudinal Data
251(1)
9.2.3 Application to the Longitudinal Partial Linear Regression Model
251(1)
9.2.4 Empirical Likelihood Approach for Marginal Likelihood Functions
252(3)
9.2.5 Empirical Likelihood in the Linear Regression Framework with Surrogate Covariates
255(2)
9.3 Empirical Likelihood Based on Censored Data
257(8)
9.3.1 Testing the Hazard Function
257(2)
9.3.2 Estimating the Quantile Function
259(1)
9.3.3 Testing the Mean Survival Time
260(2)
9.3.4 Mean Quality-Adjusted Lifetime with Censored Data
262(1)
9.3.5 Regression Approach for the Censored Data
263(2)
9.4 Empirical Likelihood with Missing Data
265(5)
9.4.1 Fully Observed Data Case
265(1)
9.4.2 Using Imputation
266(2)
9.4.3 Incorporating Missing Probabilities
268(2)
9.4.4 Missing Covariates
270(1)
9.5 Empirical Likelihood in Survey Sampling
270(7)
9.5.1 Pseudo-Empirical Log-Likelihood Approach
270(4)
9.5.2 Many Zero Values Problem in Survey Sampling
274(3)
References 277(14)
Name Index 291(4)
Subject Index 295
Albert Vexler obtained his Ph.D. degree in Statistics and Probability Theory from the Hebrew University of Jerusalem in 2003. Dr. Vexler was a postdoctoral research fellow in the Biometry and Mathematical Statistics Branch at the National Institutes of Health, USA. Dr. Vexler is a tenured Full Professor at the SUNY, Department of Biostatistics. Dr. Vexler has authored and co-authored various publications that contribute to both the theoretical and applied aspects of statistics.

Dr. Yu received her Ph.D. degree in Statistics from Texas A & M University in 2003. Her Ph.D. advisor was Thomas E. Wehrly, Ph.D. Currently, Dr. Yu is a tenured associate Professor at the State University of New York at Buffalo, Department of Biostatistics. Also, Dr. Yu is the director of the Population Health Observatory, School of Public Health and Health Professions at the State University of New York at Buffalo.