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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Formato: Electrónico eBook
Idioma:Inglés
Publicado: World Scientific 2009.
Temas:
Probabilities.
Statistics.
Probability
Probabilités.
Statistique.
probability.
statistics.
Probabilities
Statistics
Electronic resource.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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.

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