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Scientific article
English

On the relationship between empirical likelihood and empirical saddlepoint approximation for multivariate M-estimators

Published inBiometrika, vol. 80, no. 2, p. 329-338
Publication date1993
Abstract

By comparing the expansions of the empirical log-likelihood ratio and the empirical cumulant generating function calculated at the saddlepoint, we investigate the relationship between empirical likelihood and empirical saddlepoint approximations. This leads to a nonparametric approximation of the density of a multivariate M-estimator based on the empirical likelihood and, on the other hand, it provides nonparametric confidence regions based on the empirical cumulant generating function. Some examples illustrate the use of the empirical likelihood in saddlepoint approximations and vice versa.

Keywords
  • Empirical bootstrap likelihood
  • Empirical likelihood
  • Influence function
  • M-estimator
  • Nonparametric confidence regions
  • Saddlepoint approximation
  • Small sample asymptotics
Citation (ISO format)
MONTI, Anna Clara, RONCHETTI, Elvezio. On the relationship between empirical likelihood and empirical saddlepoint approximation for multivariate M-estimators. In: Biometrika, 1993, vol. 80, n° 2, p. 329–338. doi: 10.1093/biomet/80.2.329
Identifiers
ISSN of the journal0006-3444
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