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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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|
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