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A review of differentiability in relation to robustness with application to seismic data analysis

Clarke, B.R. (2000) A review of differentiability in relation to robustness with application to seismic data analysis. Proceedings of the Indian National Science Academy, 66, A (5). pp. 467-482.

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    Abstract

    The introduction of the Frechet derivative into statistics from the mathematical literature has spomed a wealth of study of the relationships between robust statistics and mathematical• derivatives. The current view is that differentiability of the Frechet type with respect to the supremum norm is a valid approach and necessarily some well known statistics such as the arithmetic mean and the median do not have the attribute of differentiability in this sense. As an illustration of a Frechet differentiable estimating functional an L2 minimum distance estimator is applied to some data collected from seismic analysis and this provides estimates in an area where estimation previously was ad hoc and estimation was not always possible. The theoretical estimation techniques known from the study of mixtures of normal distributions are applied to this data and illustrate some of the features of using robust techniques as opposed to always resorting to the maximum likelihood estimation methods.

    Publication Type: Journal Article
    Murdoch Affiliation: School of Chemical and Mathematical Science
    Publisher: Indian National Science Academy
    URI: http://researchrepository.murdoch.edu.au/id/eprint/4790
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