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Celebrating StatisticsPapers in honour of Sir David Cox on his 80th birthday$
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A. C. Davison, Yadolah Dodge, and N. Wermuth

Print publication date: 2005

Print ISBN-13: 9780198566540

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198566540.001.0001

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On non-parametric statistical methods

On non-parametric statistical methods

Chapter:
(p.137) 6 On non-parametric statistical methods
Source:
Celebrating Statistics
Author(s):

Peter Hall (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198566540.003.0007

This chapter describes some contemporary topics in non-parametric statistics and outlines their relation to computation, particularly some topics on pure mathematics. It opens with a brief comparison of parametric and non-parametric views of the same statistical problems and some comments on the ‘two cultures’ sometimes said to exist within statistical modeling. The impact of computational advances on non-parametric statistics is discussed, and the view that raw computer power can replace theoretical consideration of a problem is firmly rebutted. The discussion then turns to the relation between mathematics, particularly pure mathematics, and statistics. The contributions made by number theory, algebraic geometry, and operator theory to some statistical problems are exemplified in the contexts of digitizing data on a lattice, estimating multiperiodic functions, errors in variables, mixture modeling, and functional principal component analysis.

Keywords:   algebraic geometry, computation, errors in variables, mixture model, multiperiodic function, number theory, operator theory, principal component analysis, pure mathematics

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