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Perspectives In Mathematical Science I : Probability And Statistics.
This book presents a collection of invited articles by distinguished probabilists and statisticians on the occasion of the Platinum Jubilee Celebrations of the Indian Statistical Institute - a notable institute with significant achievement in research areas of statistics, probability and mathematics...
| Clasificación: | Libro Electrónico |
|---|---|
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
World Scientific
2009.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 245 | 0 | 0 | |a Perspectives In Mathematical Science I : |b Probability And Statistics. |
| 260 | |b World Scientific |c 2009. | ||
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| 505 | 0 | |a Cover13; -- Contents -- Foreword -- Preface -- 1. Entropy and Martingale K.B. Athreya and M.G. Nadkarni -- 1.1. Introduction -- 1.2. Relative Entropy and Gibbs-Boltzmann Measures -- 1.2.1. Entropy Maximization Results -- 1.2.2. Weak Convergence of Gibbs-Boltzmann Distribution -- 1.2.3. Relative Entropy and Conditioning -- 1.3. Measure Free Martingales, Weak Martingales, Martingales -- 1.3.1. Finite Range Case -- 1.3.2. The General Case -- 1.4. Equivalent Martingale Measures -- References -- 2. Marginal Quantiles: Asymptotics for Functions of Order Statistics G.J. Babu -- 2.1. Introduction -- 2.1.1. Streaming Data -- 2.2. Marginal Quantiles -- 2.2.1. Joint Distribution of Marginal Quantiles -- 2.2.2. Weak Convergence of Quantile Process -- 2.3. Regression under Lost Association -- 2.4. Mean of Functions of Order Statistics -- 2.5. Examples -- Acknowledgment -- References -- 3. Statistics on Manifolds with Applications to Shape Spaces R. Bhattacharya and A. Bhattacharya -- 3.1. Introduction -- 3.2. Geometry of Shape Manifolds -- 3.2.1. The Real Projective Space RPd -- 3.2.2. Kendalls (Direct Similarity) Shape Spaces 931;k -- 3.2.3. Reflection (Similarity) Shape Spaces RSk m -- 3.2.4. Affine Shape Spaces ASk m -- 3.2.5. Projective Shape Spaces P931;k13;10;m -- 3.3. Fr180;echet Means on Metric Spaces -- 3.4. Extrinsic Means on Manifolds -- 3.4.1. Asymptotic Distribution of the Extrinsic Sample Mean -- 3.5. Intrinsic Means on Manifolds -- 3.6. Applications -- 3.6.1. Sd -- 3.6.2. RPd -- 3.6.3. 931;k m -- 3.6.4. 931;k2 -- 3.6.5. R931;k m -- 3.6.6. A931;k m -- 3.6.7. P0931;k m -- 3.7. Examples -- 3.7.1. Example 1: Gorilla Skulls -- 3.7.2. Example 2: Schizophrenic Children -- 3.7.3. Example 3: Glaucoma Detection -- Acknowledgment -- References -- 4. Reinforcement Learning 8212; A Bridge Between Numerical Methods and Monte Carlo V.S. Borkar -- 4.1. Introduction -- 4.2. Stochastic Approximation -- 4.3. Estimating Stationary Averages -- 4.4. Function Approximation -- 4.5. Estimating Stationary Distribution -- 4.6. Acceleration Techniques -- 4.7. Future Directions -- References -- 5. Factors, Roots and Embeddings of Measures on Lie Groups S.G. Dani -- 5.1. Introduction -- 5.2. Some Basic Properties of Factors and Roots -- 5.3. Factor Sets -- 5.4. Compactness -- 5.5. Roots -- 5.6. One-Parameter Semigroups -- References -- 6. Higher Criticism in the Context of Unknown Distribution, Non-independence and Classi.cation A. Delaigle and P. Hall -- 6.1. Introduction -- 6.2. Methodology -- 6.2.1. Higher-criticism signal detection -- 6.2.2. Generalising and adapting to an unknown null distribution -- 6.2.3. Classifiers based on higher criticism -- 6.3. Theoretical Properties -- 6.3.1. Effectiveness of approximation to hcW by hcW -- 6.3.2. Removing the assumption of independence -- 6.3.3. Delineating good performance -- 6.4. Further Results -- 6.4.1. Alternative constructions of hcW and hcW -- 6.4.2. Advantages of incorporating the threshold -- 6.5. Numerical Properties in the Case of Classification -- 6.6. Technical Arguments -- 6.6.1. Proof of Theorem 6.1 -- 6.6.2. Proof of Theorem 6.2 -- References -- Appendix -- A.1. Description of the Cross-Validation Procedure -- A.2. Proof of Theorem 6.3. | |
| 520 | |a This book presents a collection of invited articles by distinguished probabilists and statisticians on the occasion of the Platinum Jubilee Celebrations of the Indian Statistical Institute - a notable institute with significant achievement in research areas of statistics, probability and mathematics - in 2007. With a wide coverage of topics in probability and statistics, the articles provide a current perspective of different areas of research, emphasizing the major challenging issues. The book also proves its reference and utility value for practitioners as the articles in Statistics contain. | ||
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Probabilities. | |
| 650 | 0 | |a Statistics. | |
| 650 | 2 | |a Probability | |
| 650 | 6 | |a Probabilités. | |
| 650 | 6 | |a Statistique. | |
| 650 | 7 | |a probability. |2 aat | |
| 650 | 7 | |a statistics. |2 aat | |
| 650 | 7 | |a Probabilities |2 fast | |
| 650 | 7 | |a Statistics |2 fast | |
| 655 | 4 | |a Electronic resource. | |
| 720 | |a Sastry N S Narasimha Et Al. | ||
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=1679630 |z Texto completo |
| 938 | |a EBL - Ebook Library |b EBLB |n EBL1679630 | ||
| 938 | |a ProQuest MyiLibrary Digital eBook Collection |b IDEB |n 275809 | ||
| 994 | |a 92 |b IZTAP | ||