On the Consistency of a Class of Nonlinear Regression Estimators

Asheber Abebe, Joseph W. McKean, Huybrechts F. Bindele

Abstract


In this paper, we study conditions sufficient for strong consistency of a class of estimators of parameters of nonlinear regression models. The study considers continuous functions depending on a vector of parameters and a set of random regressors. The estimators chosen are minimizers of a generalized form of the signed-rank norm. The generalization allows us to make consistency statements about minimizers of a wide variety of norms including the L1 and L2 norms. By implementing trimming, it is shown that high breakdown estimates can be obtained based on the proposed dispersion function.


Keywords


Nonlinear regression, Signed-rank, Order statistics, Strong consistency.

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DOI: http://dx.doi.org/10.18187/pjsor.v8i3.526

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Title

On the Consistency of a Class of Nonlinear Regression Estimators

Keywords

Nonlinear regression, Signed-rank, Order statistics, Strong consistency.

Description

In this paper, we study conditions sufficient for strong consistency of a class of estimators of parameters of nonlinear regression models. The study considers continuous functions depending on a vector of parameters and a set of random regressors. The estimators chosen are minimizers of a generalized form of the signed-rank norm. The generalization allows us to make consistency statements about minimizers of a wide variety of norms including the L1 and L2 norms. By implementing trimming, it is shown that high breakdown estimates can be obtained based on the proposed dispersion function.


Date

2012-07-01

Identifier


Source

Pakistan Journal of Statistics and Operation Research; Vol 8. No. 3, 2012



Print ISSN: 1816-2711 | Electronic ISSN: 2220-5810