+612 9045 4394
The Theory of Canonical Moments with Applications in Statistics, Probability, and Analysis : Wiley Series in Probability and Statistics - Holger Dette

The Theory of Canonical Moments with Applications in Statistics, Probability, and Analysis

Wiley Series in Probability and Statistics

Hardcover Published: 8th September 1997
ISBN: 9780471109914
Number Of Pages: 324

Share This Book:


RRP $301.95
or 4 easy payments of $59.48 with Learn more
Ships in 5 to 9 business days

The fascinating world of canonical moments--a unique look at this practical, powerful statistical and probability tool

Unusual in its emphasis, this landmark monograph on canonical moments describes the theory and application of canonical moments of probability measures on intervals of the real line and measures on the circle. Stemming from the discovery that canonical moments appear to be more intrinsically related to the measure than ordinary moments, the book's main focus is the broad application of canonical moments in many areas of statistics, probability, and analysis, including problems in the design of experiments, simple random walks or birth and death chains, and in approximation theory.

The book begins with an explanation of the development of the theory of canonical moments for measures on intervals a, b] and then describes the various practical applications of canonical moments. The book's topical range includes:

  • Definition of canonical moments both geometrically and as ratios of Hankel determinants
  • Orthogonal polynomials viewed geometrically as hyperplanes to moment spaces
  • Continued fractions and their link between ordinary moments and canonical moments
  • The determination of optimal designs for polynomial regression
  • The relationships between canonical moments, random walks, and orthogonal polynomials
  • Canonical moments for the circle or trigonometric functions

Finally, this volume clearly illustrates the powerful mathematical role of canonical moments in a chapter arrangement that is as logical and interdependent as is the relationship of canonical moments to statistics, probability, and analysis.

Canonical Moments.

Orthogonal Polynomials.

Continued Fractions and the Stieltjes Transform.

Special Sequences of Canonical Moments.

Canonical Moments and Optimal Design--First Applications.

Discrimination and Model Robust Designs.

Applications in Approximation Theory.

Canonical Moments and Random Walks.

The Circle and Trigonometric Functions.

Further Applications.



ISBN: 9780471109914
ISBN-10: 0471109916
Series: Wiley Series in Probability and Statistics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 324
Published: 8th September 1997
Country of Publication: US
Dimensions (cm): 24.3 x 16.3  x 2.2
Weight (kg): 0.73
Edition Number: 1