Analytic perturbations and systematic bias in statistical modeling and inference

Details Analytic perturbations and systematic bias in statistical modeling and inference Analytic perturbations and systematic bias in statistical modeling and inference

2008-05-15

arxiv.org/abs/0805.2228v1

IMS Collections 2008, Vol. 1, 17-34

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/193940307000000022 the IMS Collections (http://www.imstat.org/publications/imscollec

Scientific paper

10.1214/193940307000000022

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.

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