05476nam 2200673Ia 450 991078071570332120230721024351.01-282-75809-89786612758096981-4273-63-5(CKB)2490000000001582(EBL)1679630(OCoLC)729020092(SSID)ssj0000440718(PQKBManifestationID)11273936(PQKBTitleCode)TC0000440718(PQKBWorkID)10491239(PQKB)11311314(MiAaPQ)EBC1679630(WSP)00007308(Au-PeEL)EBL1679630(CaPaEBR)ebr10422504(CaONFJC)MIL275809(EXLCZ)99249000000000158220090806d2009 uy 0engurcn|||||||||txtccrPerspectives in mathematical sciencesI[electronic resource] /editors, N.S. Narasimha Sastry ... [et al.] ; series editor: Sankar K. PalSingapore ;London World Scientificc20091 online resource (283 p.)Statistical science and interdisciplinary research ;v. 7"Platinum jubilee series".981-4273-62-7 Includes bibliographical references.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 Data2.2. 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 m3.2.5. 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 Children3.7.3. 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 SemigroupsReferences 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 hcW6.4.2. Advantages of incorporating the thresholdThis 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 containStatistical science and interdisciplinary research ;v. 7.ProbabilitiesStatisticsProbabilities.Statistics.510519.2Narasimha Sastry N. S1583521MiAaPQMiAaPQMiAaPQBOOK9910780715703321Perspectives in mathematical sciences3866679UNINA