Weighted Bootstrap

Häftad, Engelska, 1995

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This monograph presents an account of the asymptotic behaviour of the weighted bootstrap - a new and powerful statistical technique. Researchers and advanced graduate students studying bootstrap methods will find this a valuable technical survey which is thorough and rigorous. The main aim of this book is to answer two questions: How well does the generalized bootstrap work? What are the differences between all the different weighted schemes? Readers are assumed to have already some familiarity with the bootstrap, but otherwise the account is as self-contained as possible. Proofs are presented in detail, though some lengthy calculations are deferred to appendices.

Produktinformation

Utgivningsdatum1995-02-24
Mått155 x 235 x 14 mm
Vikt376 g
FormatHäftad
SpråkEngelska
SerieLecture Notes in Statistics
Antal sidor230
FörlagSpringer-Verlag New York Inc.
ISBN9780387944784

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Table.- I.1) Introduction.- I.2) Some connected works.- I) Asymptotic theory for the generalized bootstrap of statistical differentiate functionals.- I.1) Introduction.- I.2) Fréchet-differentiability and metric indexed by a class of functions.- I.3) Consistency of the generalized bootstrapped distribution, variance estimation and Edgeworth expansion.- I.4) Applications.- I.5) Some simulation results.- II) How to choose the weights.- II.1) Introduction.- II.2) Weights generated from an i.i.d. sequence : almost sure results.- II.3) Best weights for the bootstrap of the mean via Edgeworth expansion.- II.4) Choice of the weights for general functional via Edgeworth expansion.- II.5) Coverage probability for the weighted bootstrap of general functional.- II.6) Conditional large deviations.- II.7) Conclusion.- III) Some special forms of the weighted bootstrap.- III.1) Introduction.- III.2) Bootstrapping an empirical d.f. when parameters are estimated or under some local alternatives.- III.3) Bootstrap of the extremes and bootstrap of the mean in the infinite variance case.- III.4) Conclusion.- IV) Proofs of results of Chapter I.- IV.1) Proof of Proposition I.2.1.- IV.2) Proof of Proposition I.2.2.- IV.3) Proof of Theorem I.3.1.- IV.4) Some notations and auxilliary lemmas.- IV.5) Proof of Theorem I.3.2.- IV.6) More lemmas to prove Theorem I.3.2.- IV.7) Proof of Theorem I.3.3.- IV.8) Proof of Theorem I.3.4.- IV.9) Proof of Theorem I.3.5.- V) Proofs of results of Chapter II.- V.1) Proofs of results of section II. 2.- V.2) Proof of Formula (II.3.2).- V.3) Proof of Proposition II.4.1.- V.4) Proof of (II.5.6).- V.5) Proof of (II.5.9).- V.6) Proof of (II.5.10).- V.7) Proof of (II.5.11).- V.8) Proof of Theorem II.6.2.- VI) Proofs of results of Chapter III.- VI.1) Proof of TheoremIII.1.1.- VI.2) Proof of Theorem III.1.2.- VI.3) Proof of Theorem III.2.1.- VI.4) Proof of Theorem III.2.2.- Appendix 1 : Exchangeable variables of sum 1.- Appendix 5 : Finite sample asymptotic for the mean and the bootstrap mean estimator.- Appendix 6 : Weights giving an almost surely consistent bootstrapped mean.- References.- Notation index.- Author index.