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Bootstrp and Edgeworth Expansion

  • Rabi Bhattacharya
  • Manfred Denker
Chapter
Part of the DMV Seminar book series (OWS, volume 14)

Abstract

Suppose that T(P) is a functional, say real valued, on some subset P of the set of all probability measures on a measurable space (χ, B), and one wishes to obtain a confidence interval for T(P) based on n i.i.d. observations X 1 ,..., X n with common distribution P. For example, if P is a parametric family then T(P) is a function of the parameter, and one may use the maximum likelihood estimator θ̂ of T(P) and an estimate s n of its standard error σ n to form a confidence interval using normal approximation. Under appropriate assumptions (stated below) one may do better than normal approximation for the studentized statistic \( ({\hat{\theta }_{n}} - T(P))/{s_{n}} \). In this subsection we consider two procedures for improvement over the normal approximation: (1) the bootstrap proposed by Efron [36], and (2) the empirical Edgeworth expansion.

Keywords

Maximum Likelihood Estimator Normal Approximation Common Distribution Borel Measurable Function Sample Moment 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag Basel 1990

Authors and Affiliations

  • Rabi Bhattacharya
    • 1
  • Manfred Denker
    • 2
  1. 1.Department of MathematicsIndiana UniversityBloomingtonUSA
  2. 2.Institut für MathematischeStochastikGöttingenGermany

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