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Asymptotic variance of M-estimators for dependent Gaussian random variables

✍ Scribed by Marc G. Genton

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
313 KB
Volume
38
Category
Article
ISSN
0167-7152

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✦ Synopsis

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.

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This paper discusses the consistency in the strong sense and essential uniqueness of M -estimation for dependent random variables. The hypotheses are based on the function deΓΏning implicitly the M -estimation as well as on its ΓΏrst derivative and its Hessian matrix. No explicit hypotheses on the ran