Analytic perturbations and systematic bias in staistical modeling and inference
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Date
2008
Authors
Filar, Jerzy A
Hudson, Irene
Mathew, Thomas
Sinha, Bimal
Journal Title
Journal ISSN
Volume Title
Publisher
Institute of Mathematical Statistics
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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.
Description
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.
Keywords
Mathematics, Analytic perturbation, Design matrix, Factor analysis
Citation
Filar, J.A., Hudson, I., Mathew, T. and Sinha, B., 2008. Analytic perturbations and systematic bias in statistical modeling and inference. IMS Collection 2008, 1, 17-34.