Author | Barbe, Philippe. author |
---|---|
Title | The Weighted Bootstrap [electronic resource] / by Philippe Barbe, Patrice Bertail |
Imprint | New York, NY : Springer New York, 1995 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-2532-4 |
Descript | VIII, 230 p. online resource |
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) Frรฉchet-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 Theorem III.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