Asymptotic variance of M-estimators for dependent Gaussian random variables

Marc G. Genton*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


This paper discusses the asymptotic behavior of M-estimators for dependent Gaussian random variables. We show that for a Gaussian distribution, the asymptotic variance of an M-estimator of scale is minimal in the independent case and must necessarily increase for dependent data. This is not true for location estimation where the asymptotic variance can increase or decrease for dependent observations, depending on the sign of the correlation. Several examples are analyzed, showing that the asymptotic variance of the maximum likelihood estimator varies widely under dependencies.

Original languageEnglish (US)
Pages (from-to)255-261
Number of pages7
JournalStatistics and Probability Letters
Issue number3
StatePublished - Jun 15 1998
Externally publishedYes


  • Asymptotic efficiency
  • Asymptotic variance
  • Dependent data
  • Location
  • M-estimator
  • Robustness
  • Scale

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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