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Robust Estimators in Non-linear Regression Models with Long-Range Dependence

In: Optimal Design and Related Areas in Optimization and Statistics

Author

Listed:
  • A. Ivanov

    (National Technical University, Kyiv Polytechnic Institute)

  • N. Leonenko

Abstract

Summary We present the asymptotic distribution theory for M-estimators in non-linear regression model with long-range dependence (LRD) for a general class of covariance functions in discrete and continuous time. Our limiting distributions are not always Gaussian and they have second moments. We present non-Gaussian distributions in terms of characteristic functions rather then the multiple Ito–Wiener integrals. These results are some variants of the non-central limit theorems of Taqqu (1979), however the normalizing factors and limiting distributions are of more general type. Beran (1991) observed, in the case of a Gaussian sample with LRD, that the M-estimators and the least-squares estimator of the location parameter have equal asymptotic variances. We present a similar phenomenon for a general non-linear regression model with LRD in discrete and continuous time (see Corollary 1), that is in the case of Gaussian non-linear regression models with LRD errors the M-estimates (for smooth score functions) of the regression parameters are asymptotically equivalent in the first order to the least-squares estimator.

Suggested Citation

  • A. Ivanov & N. Leonenko, 2009. "Robust Estimators in Non-linear Regression Models with Long-Range Dependence," Springer Optimization and Its Applications, in: Luc Pronzato & Anatoly Zhigljavsky (ed.), Optimal Design and Related Areas in Optimization and Statistics, chapter 9, pages 193-221, Springer.
    • Handle: RePEc:spr:spochp:978-0-387-79936-0_9
    DOI: 10.1007/978-0-387-79936-0_9
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