Muutke küpsiste eelistusi

Theory of Canonical Moments with Applications in Statistics, Probability, and Analysis [Kõva köide]

(Purdue University, Indiana), (Ruhr-University Bochum, Germany)
  • Formaat: Hardback, 360 pages, kõrgus x laius x paksus: 243x163x22 mm, kaal: 737 g
  • Sari: Wiley Series in Probability and Statistics
  • Ilmumisaeg: 15-Sep-1997
  • Kirjastus: Wiley-Interscience
  • ISBN-10: 0471109916
  • ISBN-13: 9780471109914
Teised raamatud teemal:
Theory of Canonical Moments with Applications in Statistics, Probability, and AnalysisSuurem pilt
  • Formaat: Hardback, 360 pages, kõrgus x laius x paksus: 243x163x22 mm, kaal: 737 g
  • Sari: Wiley Series in Probability and Statistics
  • Ilmumisaeg: 15-Sep-1997
  • Kirjastus: Wiley-Interscience
  • ISBN-10: 0471109916
  • ISBN-13: 9780471109914
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780471109914.html
Märksõnad:
A monograph on canonical moments describing the theory and application of canonical moments of probability measures on intervals of the real line and, to a lesser extent, measures on the circle. Stemming from the discovery that canonical moments appear to be more intrinsically related to the measure than ordinary moments, this volume'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. Annotation c. by Book News, Inc., Portland, Or.

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.
Preface v(11)
Interdependence of
Chapters		 xvi
1. Canonical Moments
1(41)
1.1 Introduction
1(2)
1.2 Moment Spaces
3(8)
1.3 Canonical Moments
11(5)
1.4 Hankel Determinants
16(9)
1.5 Q-D Algorithm
25(7)
1.6 Statistical Design of Experiments and Maximization of the Hankel Determinants
32(3)
1.7 Canonical Moments, Continued Fractions, and Orthogonal Polynomials
35(4)
1.8 Random Walks or Birth and Death Chains
39(3)
2. Orthogonal Polynomials
42(33)
2.1 Introduction
42(7)
2.2 Support Polynomials
49(6)
2.3 Recursive Formula
55(11)
2.4 Inverse Map
66(3)
2.5 Reversed Canonical Moment Sequences
69(6)
3. Continued Fractions and the Stieltjes Transform
75(29)
3.1 Introduction
75(2)
3.2 Continued Fractions
77(8)
3.3 Continued Fraction Expansions of the Stieltjes Transform
85(6)
3.4 More Symmetry or Duality
91(2)
3.5 Canonical Moments and Roots of Polynomials
93(3)
3.6 Inversion of the Stieltjes Transform
96(8)
4. Special Sequences of Canonical Moments
104(24)
4.1 Introduction
104(1)
4.2 Simple Sequences
105(2)
4.3 Measures with "Nearly" Equal Weights
107(11)
4.4 Partitioned Sequences
118(6)
4.5 Infinite Sequences of Canonical Moments
124(4)
5. Canonical Moments and Optimal Designs--First Applications
128(42)
5.1 Introduction
128(1)
5.2 Linear Models
128(7)
5.3 Optimum Experimental Designs
135(4)
5.4 Approximate Optimal Designs
139(7)
5.5 D- and G-Optimal Designs for Univariate Polynomial Regression
146(6)
5.6 D(s)-Optimal Designs for Univariate Polynomial Regression
152(2)
5.7 XXX(p)-Optimal Designs for the Highest Two Coefficients
155(4)
5.8 Designs for Multivariate Polynomial Regression
159(11)
6. Discrimination and Model Robust Designs
170(24)
6.1 Introduction
170(1)
6.2 Discrimination Designs with Geometric Means
171(9)
6.3 Discrimination Designs Based on XXX(p)-Means
180(8)
6.4 Model Robust Designs
188(6)
7. Applications in Approximation Theory
194(26)
7.1 Introduction
194(1)
7.2 Asymptotic Zero Distribution of Orthogonal Polynomials
195(4)
7.3 Identities for Orthogonal Polynomials
199(10)
7.4 Extremal Problems for Polynomials
209(11)
8. Canonical Moments and Random Walks
220(38)
8.1 Introduction
220(2)
8.2 Random Walk Measures
222(3)
8.3 Processes with the Same Spectral Measure
235(4)
8.4 Generating Functions
239(11)
8.5 Symmetric Random Walks
250(8)
9. The Circle and Trigonometric Functions
258(33)
9.1 Introduction
258(1)
9.2 Moment Spaces and Canonical Representations
259(4)
9.3 Canonical Moments on the Circle
263(5)
9.4 Orthogonal Polynomials on the Circle
268(3)
9.5 Transforms and Continued Fractions
271(6)
9.6 Stationary Random Processes
277(5)
9.7 Limiting Prediction and Maximum Entropy
282(3)
9.8 Experimental Design for Trigonometric Regressions
285(6)
10. Further Applications
291(20)
10.1 Introduction
291(1)
10.2 Bayesian Binomial Estimation
291(4)
10.3 Canonical Moment Expressions
295(3)
10.4 Minimax Estimates in P(c(n))
298(4)
10.5 Risk Difference
302(1)
10.6 A Limit Theorem in M(n)
303(3)
10.7 More Chebyshev Polynomials
306(5)
Bibliography 311(9)
Index of Symbols 320(3)
Author Index 323(2)
Subject Index 325


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.