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
M-Estimation for dependent random variables
β Scribed by Reinhard Furrer
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 90 KB
- Volume
- 57
- Category
- Article
- ISSN
- 0167-7152
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β¦ Synopsis
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 random variables are necessary for consistency and uniqueness, thus the framework holds for any stochastic process.
π SIMILAR VOLUMES
W. Stute (Ann. Probab. 19, No. 2 (1991), 812 825) introduced a class of so-called U-statistics, which may be viewed as a generalization of the Nadaraya Watson estimates of a regression function. In this paper, we extend the results from the independent case to the dependent case.