Hilbert Space Methods in Probability and Statistical Inference

By: Christopher G. Small, Don L. McLeish

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Hardcover | 18 March 1994 | Edition Number 1

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Hardcover
268 Pages

Dimensions(cm)
23.9 x 16.15 x 1.82

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Hilbert space methods are an alternative to the measure-theoretic definitions of random-variables. They are important in the theory of martingales and stochastic integration, as well as in interpolation and density estimation. Hilbert space techniques, which include bases, subspaces, projections and orthogonal decompositions, already pervade many areas of applied mathematics and statistics, such as regression analysis and stochastic processes. The purpose of this book is to explain the use of Hilbert space methods in probability and statistics. It demonstrates how these tools also cross the boundaries into the foundation of probability and statistics. They underlie and generalize standard notions of complete sufficiency, statistical inference censorship, and loss of information. The book has evolved from class notes and other material used from courses taught by the authors at the Universities of Waterloo and Toronto. Each chapter is supplemented by an extensive set of notes and problems.

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