On non-parametric statistical methods
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.
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