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Linear Statistical Inference and Its Applications

By: Rao, C.RadhakrishnaMaterial type: Text

TextSeries: Wiley series in probability and mathematical statisticsPublication details: New York Wiley Eastern Ltd 2002Edition: 2nd edDescription: xx, 625 pagesISBN: 9780852267530 ; 0852267533Subject(s): Statistical Inference | Mathematical statistics | ProbabilitiesDDC classification: 519.54

Contents:

Ch. 1. Algebra of Vectors and Matrices -- 1a. Vector Spaces -- 1b. Theory of Matrices and Determinants -- 1c. Eigenvalues and Reduction of Matrices -- 1d. Convex Sets in Vector Spaces -- 1e. Inequalities -- 1f. Extrema of Quadratic Forms -- Ch. 2. Probability Theory, Tools and Techniques -- 2a. Calculus of Probability -- 2b. Mathematical Expectation and Moments of Random Variables -- 2c. Limit Theorems -- 2d. Family of Probability Measures and Problems of Statistics -- Ch. 3. Continuous Probability Models -- 3a. Univariate Models -- 3b. Sampling Distributions -- 3c. Symmetric Normal Distribution -- 3d. Bivariate Normal Distribution -- Ch. 4. The Theory of Least Squares and Analysis of Variance -- 4a. Theory of Least Squares (Linear Estimation) -- 4b. Tests of Hypotheses and Interval Estimation -- 4c. Problems of a Single Sample -- 4d. One-Way Classified Data -- 4e. Two-Way Classified Data -- 4f. A General Model for Two-Way Data and Variance Components -- 4g. The Theory and Application of Statistical Regression -- 4h. The General Problem of Least Squares with Two Sets of Parameters -- 4i. Unified Theory of Linear Estimation -- 4j. Estimation of Variance Components -- 4k. Biased Estimation in Linear Models -- Ch. 5. Criteria and Methods of Estimation -- 5a. Minimum Variance Unbiased Estimation -- 5b. General Procedures -- 5c. Criteria of Estimation in Large Samples -- 5d. Some Methods of Estimation in Large Samples -- 5e. Estimation of the Multinomial Distribution -- 5f. Estimation of Parameters in the General Case -- 5g. The Method of Scoring for the Estimation of Parameters -- Ch. 6. Large Sample Theory and Methods -- 6a. Some Basic Results -- 6b. Chi-Square Tests for the Multinomial Distribution -- 6c. Tests Relating to Independent Samples from Multinomial Distributions -- 6d. Contingency Tables -- 6e. Some General Classes of Large Sample Tests -- 6f. Order Statistics -- 6g. Transformation of Statistics -- 6h. Standard Errors of Moments and Related Statistics -- Ch. 7. Theory of Statistical Inference -- 7a. Testing of Statistical Hypotheses -- 7b. Confidence Intervals -- 7c. Sequential Analysis -- 7d. Problem of Identification -- Decision Theory -- 7e. Nonparametric Inference -- 7f. Ancillary Information -- Ch. 8. Multivariate Analysis -- 8a. Multivariate Normal Distribution -- 8b. Wishart Distribution -- 8c. Analysis of Dispersion -- 8d. Some Applications of Multivariate Tests -- 8e. Discriminatory Analysis (Identification) -- 8f. Relation between Sets of Variates -- 8g. Orthonormal Basis of a Random Variable.

Summary: "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.

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Item type	Current library	Collection	Call number	Status	Barcode
Reference Books	Main Library Reference	Reference	519.54 RAD (Browse shelf(Opens below))	Available	001299
Lending Books	Main Library Stacks	Permanent Reference	519.54 RAD (Browse shelf(Opens below))	Available	000173
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Includes Index

Ch. 1. Algebra of Vectors and Matrices --
1a. Vector Spaces --
1b. Theory of Matrices and Determinants --
1c. Eigenvalues and Reduction of Matrices --
1d. Convex Sets in Vector Spaces --
1e. Inequalities --
1f. Extrema of Quadratic Forms --
Ch. 2. Probability Theory, Tools and Techniques --
2a. Calculus of Probability --
2b. Mathematical Expectation and Moments of Random Variables --
2c. Limit Theorems --
2d. Family of Probability Measures and Problems of Statistics --
Ch. 3. Continuous Probability Models --
3a. Univariate Models --
3b. Sampling Distributions --
3c. Symmetric Normal Distribution --
3d. Bivariate Normal Distribution --
Ch. 4. The Theory of Least Squares and Analysis of Variance --
4a. Theory of Least Squares (Linear Estimation) --
4b. Tests of Hypotheses and Interval Estimation --
4c. Problems of a Single Sample --
4d. One-Way Classified Data --
4e. Two-Way Classified Data --
4f. A General Model for Two-Way Data and Variance Components --
4g. The Theory and Application of Statistical Regression --
4h. The General Problem of Least Squares with Two Sets of Parameters --
4i. Unified Theory of Linear Estimation --
4j. Estimation of Variance Components --
4k. Biased Estimation in Linear Models --
Ch. 5. Criteria and Methods of Estimation --
5a. Minimum Variance Unbiased Estimation --
5b. General Procedures --
5c. Criteria of Estimation in Large Samples --
5d. Some Methods of Estimation in Large Samples --
5e. Estimation of the Multinomial Distribution --
5f. Estimation of Parameters in the General Case --
5g. The Method of Scoring for the Estimation of Parameters --
Ch. 6. Large Sample Theory and Methods --
6a. Some Basic Results --
6b. Chi-Square Tests for the Multinomial Distribution --
6c. Tests Relating to Independent Samples from Multinomial Distributions --
6d. Contingency Tables --
6e. Some General Classes of Large Sample Tests --
6f. Order Statistics --
6g. Transformation of Statistics --
6h. Standard Errors of Moments and Related Statistics --
Ch. 7. Theory of Statistical Inference --
7a. Testing of Statistical Hypotheses --
7b. Confidence Intervals --
7c. Sequential Analysis --
7d. Problem of Identification --
Decision Theory --
7e. Nonparametric Inference --
7f. Ancillary Information --
Ch. 8. Multivariate Analysis --
8a. Multivariate Normal Distribution --
8b. Wishart Distribution --
8c. Analysis of Dispersion --
8d. Some Applications of Multivariate Tests --
8e. Discriminatory Analysis (Identification) --
8f. Relation between Sets of Variates --
8g. Orthonormal Basis of a Random Variable.

"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.

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