Detailansicht
The Theory of Canonical Moments with Applications in Statistics, Probability, and Analysis
Wiley Series in Probability and Statistics
ISBN/EAN: 9780471109914
Umbreit-Nr.: 2083193
Sprache:
Englisch
Umfang: 324 S.
Format in cm:
Einband:
gebundenes Buch
Erschienen am 15.09.1997
Auflage: 1/1997
- Zusatztext
- This new material is concerned with the theory and applications of probability, statistics and analysis of canonical moments. It provides a powerful tool for the determination of optimal experimental designs, for the calculation of the main characteristics of random walks, and for other moment problems appearing in probability and statistics.
- Kurztext
- 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.
- Autorenportrait
- HOLGER DETTE is Professor of Mathematics at Ruhr-Universität Bochum, Fakultät und Institut für Mathematik, Germany. WILLIAM J. STUDDEN is Professor of Statistics and Mathematics at Purdue University.