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Mahalanobis' Fractile Graphs, Monotone Index Models and Multivariate Quantiles
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When
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2.00pm on Friday 27th October
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Where
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B617, Leverhulme Library, Columbia House
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Presentations
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Speaker
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Probal Chaudhuri
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From
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Indian Statistical Institute, Calcutta
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Abstract
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Fractile graphs introduced by P. C. Mahalanobis in the middle of the 20th century are nonparametric regression tools that regress the dependent variable on the fractiles (i.e. quantiles) of the independent variables.
The use of fractiles of the independent variables leads to a universal distribution free standardization device that facilitates comparison of regression functions even if the independent variables are not in comparable scales as it happens sometimes in econometric and biostatistical applications. The problem becomes challenging in multiple regression situations when there are several independent variables, and Mahalanobis had only little success in extending the fractile curves into fractile surfaces or hyper-surfaces. Quantile regression on the other hand is a method for regressing the fractiles of the dependent variable on the independent variables. It has a fundamental connection with monotone index models that are well known in econometrics. A challenging problem there is the extension of monotone index models for multivariate response problems.
In this talk, I shall explore some intriguing links between these two problems and their possible solutions using some versions of multivariate quantiles.
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For further information
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Thomas Hewlett (Postgraduate Administrator) Ext. 6879
Department of Statistics, Columbia House
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