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

A. Ivanov () and N. Leonenko ()
Additional contact information
A. Ivanov: National Technical University, Kyiv Polytechnic Institute

Chapter 9 in Optimal Design and Related Areas in Optimization and Statistics, 2009, pp 193-221 from Springer

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.

Keywords: Linear Regression Model; Asymptotic Normality; Little Square Estimate; Robust Estimator; Nonlinear Regression Model (search for similar items in EconPapers)
Date: 2009
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-0-387-79936-0_9

Ordering information: This item can be ordered from
http://www.springer.com/9780387799360

DOI: 10.1007/978-0-387-79936-0_9

Access Statistics for this chapter

More chapters in Springer Optimization and Its Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().