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Perspectives in mathematical sciences . I / / editors, N.S. Narasimha Sastry ... [et al.] ; series editor: Sankar K. Pal



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Titolo: Perspectives in mathematical sciences . I / / editors, N.S. Narasimha Sastry ... [et al.] ; series editor: Sankar K. Pal Visualizza cluster
Pubblicazione: Singapore ; ; London, : World Scientific, c2009
Edizione: 1st ed.
Descrizione fisica: 1 online resource (283 p.)
Disciplina: 510
519.2
Soggetto topico: Probabilities
Statistics
Altri autori: Narasimha SastryN. S  
Note generali: "Platinum jubilee series".
Nota di bibliografia: Includes bibliographical references.
Nota di contenuto: 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. Kendall's (Direct Similarity) Shape Spaces Σk; 3.2.3. Reflection (Similarity) Shape Spaces RSk m; 3.2.4. Affine Shape Spaces ASk m
3.2.5. Projective Shape Spaces PΣk m3.3. Fréchet 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; 3.6.1.1. Extrinsic Mean on Sd; 3.6.1.2. Intrinsic Mean on Sd; 3.6.2. RPd; 3.6.2.1. Extrinsic Mean on RPd; 3.6.2.2. Intrinsic Mean on RPd; 3.6.3. Σk m; 3.6.4. Σk2; 3.6.4.1. Extrinsic Mean on Σk2; 3.6.4.2. Intrinsic Mean on Σk2; 3.6.5. RΣk m; 3.6.6. AΣk m; 3.6.7. P0Σk 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 - 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 Classification 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
Sommario/riassunto: 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
Titolo autorizzato: Perspectives in mathematical sciences  Visualizza cluster
ISBN: 1-282-75809-8
9786612758096
981-4273-63-5
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 9910825594203321
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Serie: Statistical science and interdisciplinary research ; ; v. 7.