The Bootstrap and Edgeworth Expansion

Bootstrap methods are among the most active areas of statistical research, and are important to those interested in statistical theory and applications. This ground-breaking reference remains a basic reference in this important area.

Autorentext

Dr Richard Edlin, PhD is a Senior Lecturer based within the Health Systems section of the School of Population Health, University of Auckland, New Zealand. Richard has published within both economics- and clinically-focused journals, including the top field journals in health economics. Much of his research involves cost-effectiveness analysis. Richard leads teaching on postgraduate cost effectiveness. Professor Christopher McCabe, PhD, holds a Capital Health Endowed Research Chair at the University of Alberta, having previously held Chairs at the Universities of Leeds, Warwick and Sheffield. He is on the health economics working group for Canadian Agency for Drugs and Technologies in Health (CADTH). He has acted as a consultant for public and private sector organizations in Europe, North America and Australasia; most notably with NICE in the UK. His primary research interest is in the development of efficient research and development processesfor biotherapies and devices in the context of value based reimbursement market access hurdles. Professor Claire Hulme, PhD, holds a Chair in Health Economics and is head of the Academic Unit of Health Economics at the University of Leeds. She is on the National Institute of Health Research Health Technology Assessment Commissioning Panel in the UK. Her research interests lie in the economic evaluation of community programmes spanning the health and social care sectors, particularly economic evaluation alongside clinical trials. Dr Peter Hall, MBChB, PhD, is a Senior Clinical Lecturer at the University of Edinburgh and a visiting Health Economist at the University of Leeds. He practices as a medical oncologist with an interest in breast cancer. His research interests include the use routine healthcare data, clinical pathway analysis and Bayesian decision modelling to inform efficient research design. He has an interest in the economic evaluation of diagnostic tests and personalised medicine strategies. He is a past National Institute of Health and Clinical Excellence Scholar. Judy Wright, MSc is a Senior Information Specialist and a qualified Librarian. Within her current role she leads the development of health research information support with a team of Information Specialists located within the Academic Unit of Health Economics, University of Leeds. Judy manages a portfolio of activities supporting health economics research that includes custom-made literature searching, reference management and search methodology advice.

Zusammenfassung
Secondly, it gives an account of Edgeworth expansion. The first two chapters deal with the bootstrap and Edgeworth expansion respectively, while chapters 3 and 4 bring these two themes together, using Edgeworth expansion to explore and develop the properties of the bootstrap.

Inhalt
1: Principles of Bootstrap Methodology.- 2: Principles of Edgeworth Expansion.- 3: An Edgeworth View of the Bootstrap.- 4: Bootstrap Curve Estimation.- 5: Details of Mathematical Rigour.- Appendix I: Number and Sizes of Atoms of Nonparametric Bootstrap Distribution.- Appendix II: Monte Carlo Simulation.- II.1 Introduction.- II.2 Uniform Resampling.- II.3 Linear Approximation.- II.4 Centring Method.- II.5 Balanced Resampling.- II.6 Antithetic Resampling.- II.7 Importance Resampling.- II.7.1 Introduction.- II.7.2 Concept of Importance Resampling.- II.7.3 Importance Resampling for Approximating Bias, Variance, Skewness, etc..- II.7.4 Importance Resampling for a Distribution Function.- II.8 Quantile Estimation.- Appendix III: Confidence Pictures.- Appendix IV: A Non-Standard Example: Quantite Error Estimation.- IV. 1 Introduction.- IV.2 Definition of the Mean Squared Error Estimate.- IV.3 Convergence Rate of the Mean Squared Error Estimate.- IV.4 Edgeworth Expansions for the Studentized Bootstrap Quantile Estimate.- Appendix V: A Non-Edgeworth View of the Bootstrap.- References.- Author Index.