Bootstrap Methods and their Application Anthony Davison c2006 A short course based on the book ‘Bootstrap Methods and their Application’, by A. C. Davison and D. V. ambridge University Press, 1997 Anthony Davison: Bootstrap Methods and their Application, 1 Summary ?Bootstrap: simulation methods for frequentist inference. ?Useful when ?standard assumptions invalid (nsmall, data not normal, . . .); ?standard problem has non-standard twist; ?complex problem has no (reliable) theory; ?or (almost) anywhere else. ?Aim to describe ?basic ideas; ?con?dence intervals; ?tests; ?some approaches for regression Anthony Davison: Bootstrap Methods and their Application, 2 Motivation ?Motivation ?Basic notions ?Con?dence intervals ?Several samples ?Variance estimation ?Tests ?Regression Anthony Davison: Bootstrap Methods and their Application, 3 Motivation AIDS data ?UK AIDS diagnoses 1988–1992. ?Reporting delay up to several years! ?Problem: predict state of epidemic at end 1992, with realistic statement of uncertainty. ?Simple model: number of reports in rowjand columnk Poisson, mean μ jk= exp(α j+β k). ?Unreported diagnoses in periodjPoisson, mean X kunobs μ jk= exp(α j) X kunobs exp(β k). ?Estimate total unreported diagnoses from periodjby replacingα jandβ kby MLEs. ?How reliable are these predictions? ?How sensible is the Poisson model? Anthony Davison: Bootstrap Methods and their Application, 4 Motivation Diagnosis Reporting-delay interval (quarters): Total period reports to end Year Quarter 0 1 2 3 4 5 6 · · · ≥14 of 1992 1988 1 31 80 16 9 3 2 8 · · · 6 174 2 26 99 27 9 8 11 3 · · · 3 211 3 31 95 35 13 18 4 6 · · · 3 224 4 36 77 20 26 11 3 8 · · · 2 205 1989 1 32 92 32 10 12 19 12 · · · 2 224 2 15 92 14 27 22 21 12 · · · 1 219 3 34 104 29 31 18 8 6 · · · 253 4 38 101 34 18 9 15 6 · · · 233 1990 1 31 124 47 24 11 15 8 · · · 281 2 32 132 36 10 9 7 6 · · · 245 3 49 107 51 17 15 8 9 · ·
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