LEADER 05509nam 2200685Ia 450 001 9910456150303321 005 20200520144314.0 010 $a1-282-75809-8 010 $a9786612758096 010 $a981-4273-63-5 035 $a(CKB)2490000000001582 035 $a(EBL)1679630 035 $a(OCoLC)729020092 035 $a(SSID)ssj0000440718 035 $a(PQKBManifestationID)11273936 035 $a(PQKBTitleCode)TC0000440718 035 $a(PQKBWorkID)10491239 035 $a(PQKB)11311314 035 $a(MiAaPQ)EBC1679630 035 $a(WSP)00007308 035 $a(Au-PeEL)EBL1679630 035 $a(CaPaEBR)ebr10422504 035 $a(CaONFJC)MIL275809 035 $a(EXLCZ)992490000000001582 100 $a20090806d2009 uy 0 101 0 $aeng 135 $aurcn||||||||| 181 $ctxt 182 $cc 183 $acr 200 00$aPerspectives in mathematical sciences$hI$b[electronic resource] /$feditors, N.S. Narasimha Sastry ... [et al.] ; series editor: Sankar K. Pal 210 $aSingapore ;$aLondon $cWorld Scientific$dc2009 215 $a1 online resource (283 p.) 225 1 $aStatistical science and interdisciplinary research ;$vv. 7 300 $a"Platinum jubilee series". 311 $a981-4273-62-7 320 $aIncludes bibliographical references. 327 $aContents; 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 327 $a2.2. 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 ?k; 3.2.3. Reflection (Similarity) Shape Spaces RSk m; 3.2.4. Affine Shape Spaces ASk m 327 $a3.2.5. Projective Shape Spaces P?k m3.3. Fre?chet 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. ?k m; 3.6.4. ?k2; 3.6.4.1. Extrinsic Mean on ?k2; 3.6.4.2. Intrinsic Mean on ?k2; 3.6.5. R?k m; 3.6.6. A?k m; 3.6.7. P0?k m; 3.7. Examples; 3.7.1. Example 1: Gorilla Skulls; 3.7.2. Example 2: Schizophrenic Children 327 $a3.7.3. 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 327 $aReferences 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 327 $a6.4.2. Advantages of incorporating the threshold 330 $aThis book presents a collection of invited articles by distinguished probabilists and statisticians on the occasion of the Platinum Jubilee Celebrations of the Indian Statistical Institute - a notable institute with significant achievement in research areas of statistics, probability and mathematics - in 2007. With a wide coverage of topics in probability and statistics, the articles provide a current perspective of different areas of research, emphasizing the major challenging issues. The book also proves its reference and utility value for practitioners as the articles in Statistics contain 410 0$aStatistical science and interdisciplinary research ;$vv. 7. 606 $aProbabilities 606 $aStatistics 608 $aElectronic books. 615 0$aProbabilities. 615 0$aStatistics. 676 $a510 676 $a519.2 701 $aNarasimha Sastry$b N. S$0984763 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910456150303321 996 $aPerspectives in mathematical sciences$92250263 997 $aUNINA