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Multivariate Expansions

  • John E. Kolassa
Part of the Lecture Notes in Statistics book series (LNS, volume 88)

Abstract

Edgeworth and saddlepoint expansions also have analogues for distributions of random vectors. As in the univariate case these expansions will be derived with reference to characteristic functions and cumulant generating functions, and hence these will be defined first. Subsequently Edgeworth density approximations will be defined. Just as in the univariate case, the Edgeworth approximation to probabilities that a random vector lies in a set is the integral of the Edgeworth density over that set; however, since sets of interest are usually not rectangular, theorems for the asymptotic accuracy of these approximations are difficult to prove. These proofs are not presented here. Approximation for variables on a multivariate lattice are discussed. Multivariate saddlepoint approximations are also defined, by a multivariate extension of steepest descent methods. These methods are also used to approximate conditional probabilities.

Keywords

Cumulative Distribution Function Random Vector Univariate Case Hermite Polynomial Saddlepoint Approximation 
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

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • John E. Kolassa
    • 1
  1. 1.Department of Biostatistics, School of Medicine and DentistryUniversity of RochesterRochesterUSA

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