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Wiley Series in Probability and Statistics Ser.: Linear Statistical Inference and Its Applications by C. Radhakrishna Rao (1973, Hardcover)

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About this product

Product Identifiers

PublisherWiley & Sons, Incorporated, John

ISBN-100471708232

ISBN-139780471708230

eBay Product ID (ePID)630070

Product Key Features

Number of Pages656 Pages

Publication NameLinear Statistical Inference and Its Applications

LanguageEnglish

SubjectProbability & Statistics / General

Publication Year1973

TypeTextbook

AuthorC. Radhakrishna Rao

Subject AreaMathematics

SeriesWiley Series in Probability and Statistics Ser.

FormatHardcover

Dimensions

Item Height1.5 in

Item Weight34 Oz

Item Length9.3 in

Item Width6.3 in

Additional Product Features

Edition Number2

Intended AudienceScholarly & Professional

LCCN72-013093

Series Volume Number22

IllustratedYes

Dewey Decimal519.5

Table Of ContentChapter 1: Algebra of Vectors and Matrices. Vector Spaces. 1a.1 Definition of Vector Spaces and Subspaces. 1a.2 Basis of a Vector Space. 1a.3 Linear Equations. 1a.4 Vector Spaces with an Inner Product. Complements and Problems. lb. Theory of Matrices and Determinants. 1b.1 Matrix Operations. 1b.2 Elementary Matrices and Diagonal Reduction of a Matrix. b.3 Determinants. 1b.4 Transformations. 1b.5 Generalized Inverse of a Matrix. 1b.6 Matrix Representation, of Vector Spaces, Bases, etc. 1b.7 Idempotent Matrices. 1b.8 Special Products of Matrices. Complements and Problems. 1c. Eigenvalues and Reduction of Matrices. 1c.1 Classification and Transformation of Quadratic Forms. 1c.2 Roots of Determinantal Equations. 1c.3 Canonical Reduction of Matrices. 1c.4 Projection Operator. 1c.5 Further Results on g-Inverse. 1c.6 Restricted Eigenvalue Problem. 1d. Convex Sets in Vector Spaces. 1d.1 Definitions. 1d.2 Separation Theorems for Convex Sets. 1e. Inequalities. 1e.1 Cauchy-Schwarz (C-S) Inequality. 1e.2 Holder's Inequality. 1e.3 Hadamard's Inequality. 1e.4 Inequalities Involving Moments. 1e.5 Convex Functions and Jensen's Inequality. 1e.6 Inequalities in Information Theory. 1e.7 Stirling's Approximation. 1f. Extrema of Quadratic Forms. 1f.1 General Results. 1f. 2 Results Involving Eigenvalues and Vectors. 1f. 3 Minimum Trace Problems. Complements and Problems. Chapter 2: Probability Theory, Tools and Techniques. 2a. Calculus of Probability. 2a.l The Space of Elementary Events. 2a.2 The Class of Subsets (Events). 2a.3 Probability as a Set Function. 2a.4 Borel Field (&sigma-field) and Extension of Probability Measure. 2a.5 Notion of a Random Variable and Distribution Function. 2a.6 Multidimensional Random Variable. 2a. 7 Conditional Probability and Statistical Independence. 2a.8 Conditional Distribution of a Random Variable. 2b. Mathematical Expectation and Moments of Random Variables. 2b.1 Properties of Mathematical Expectation. 2b.2 Moments, 2b.3 Conditional Expectation. 2b.4 Characteristic Function (c.f.). 2b.5 Inversion Theorems. 2b.6 Multivariate Moments. 2c. Limit Theorems. 2c.1 Kolmogorov Consistency Theorem. 2c.2 Convergence of a Sequence of Random Variables. 2c.3 Law of Large Numbers. 2c.4 Convergence of a Sequence of Distribution Functions. 2c.5 Central Limit Theorems. 2c.6 Sums of Independent Random Variables. 2d. Family of Probability Measures and Problems of Statistics. 2d.1 Family of Probability Measures. 2d.2 The Concept of a Sufficient Statistic. 2d.3 Characterization of Sufficiency. Appendix 2A. Stieltjes and Lebesgue Integrals. Appendix 2B. Some Important Theorems in Measure Theory and Integration. Appendix 2C. Invariance. Appendix 2D. Statistics, Subfields, and Sufficiency. Appendix 2E. Non-Negative Definiteness of a Characteristic Function. Complements and Problems Chapter 3: Continuous Probability Models. 3a. Univariate Models. 3a.1 Normal Distribution. 3a.2 Gamma Distribution. 3a.3 Beta Distribution. 3a.4 Cauchy Distribution. 3a.5 Student's t Distribution. 3a.6 Distributions Describing Equilibrium States in Statistical Mechanics. 3a.7 Distribution on a Circle. 3b. Sampling Distributions. 3b.1 Definitions and Results. 3b.2 Sum of Squares of Normal Variables. 3b.3 Joint Distribution of the Sample Mean and Variance. 3b.4 Distribution of Quadratic Forms. 3b.5 Three Fundamental Theorems of the least Squares Theory. 3b.

Synopsis"C. R. Rao would be found in almost any statistician's list of five outstanding workers in the world of Mathematical Statistics today. His book represents a comprehensive account of the main body of results that comprise modern statistical theory." -W. G. Cochran "[C. R. Rao is] one of the pioneers who laid the foundations of statistics which grew from ad hoc origins into a firmly grounded mathematical science." -B. Efrom Translated into six major languages of the world, C. R. Rao's Linear Statistical Inference and Its Applications is one of the foremost works in statistical inference in the literature. Incorporating the important developments in the subject that have taken place in the last three decades, this paperback reprint of his classic work on statistical inference remains highly applicable to statistical analysis. Presenting the theory and techniques of statistical inference in a logically integrated and practical form, it covers: * The algebra of vectors and matrices * Probability theory, tools, and techniques * Continuous probability models * The theory of least squares and the analysis of variance * Criteria and methods of estimation * Large sample theory and methods * The theory of statistical inference * Multivariate normal distribution Written for the student and professional with a basic knowledge of statistics, this practical paperback edition gives this industry standard new life as a key resource for practicing statisticians and statisticians-in-training., "C. R. Rao would be found in almost any statistician's list of five outstanding workers in the world of Mathematical Statistics today. His book represents a comprehensive account of the main body of results that comprise modern statistical theory." -W. G. Cochran " C. R. Rao is] one of the pioneers who laid the foundations of statistics which grew from ad hoc origins into a firmly grounded mathematical science." -B. Efrom Translated into six major languages of the world, C. R. Rao's Linear Statistical Inference and Its Applications is one of the foremost works in statistical inference in the literature. Incorporating the important developments in the subject that have taken place in the last three decades, this paperback reprint of his classic work on statistical inference remains highly applicable to statistical analysis. Presenting the theory and techniques of statistical inference in a logically integrated and practical form, it covers: * The algebra of vectors and matrices * Probability theory, tools, and techniques * Continuous probability models * The theory of least squares and the analysis of variance * Criteria and methods of estimation * Large sample theory and methods * The theory of statistical inference * Multivariate normal distribution Written for the student and professional with a basic knowledge of statistics, this practical paperback edition gives this industry standard new life as a key resource for practicing statisticians and statisticians-in-training.

LC Classification NumberQA276