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Analytic perturbations and systematic bias in statistical modeling and inference

Jerzy A. Filar, Irene Hudson, Thomas Mathew, and Bimal Sinha

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Abstract

In this paper we provide a comprehensive study of statistical inference in linear and allied models which exhibit some analytic perturbations in their design and covariance matrices. We also indicate a few potential applications. In the theory of perturbations of linear operators it has been known for a long time that the so-called “singular perturbations” can have a big impact on solutions of equations involving these operators even when their size is small. It appears that so far the question of whether such undesirable phenomena can also occur in statistical models and their solutions has not been formally studied. The models considered in this article arise in the context of nonlinear models where a single parameter accounts for the nonlinearity.

Chapter information

Source
N. Balakrishnan, Edsel A. Peña and Mervyn J. Silvapulle, eds., Beyond Parametrics in Interdisciplinary Research: Festschrift in Honor of Professor Pranab K. Sen (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2008), 17-34

Dates
First available in Project Euclid: 1 April 2008

Permanent link to this document
https://projecteuclid.org/euclid.imsc/1207058261

Digital Object Identifier
doi:10.1214/193940307000000022

Subjects
Primary: 15A99: Miscellaneous topics
Secondary: 62J99: None of the above, but in this section

Keywords
analytic perturbation design matrix eigen vectors eigen values factor analysis nonlinear models principal components robustness

Rights
Copyright © 2008, Institute of Mathematical Statistics

Citation

Filar, Jerzy A.; Hudson, Irene; Mathew, Thomas; Sinha, Bimal. Analytic perturbations and systematic bias in statistical modeling and inference. Beyond Parametrics in Interdisciplinary Research: Festschrift in Honor of Professor Pranab K. Sen, 17--34, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2008. doi:10.1214/193940307000000022. https://projecteuclid.org/euclid.imsc/1207058261


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