Linear Statistical Inference and Its Applications
Rao, C.Radhakrishna
Linear Statistical Inference and Its Applications - 2nd ed. - New York Wiley Eastern Ltd 2002. - xx, 625 pages ; - Wiley series in probability and mathematical statistics. .
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.
9780852267530 0852267533
Statistical Inference
Mathematical statistics.
Probabilities
519.54 / RAO
Linear Statistical Inference and Its Applications - 2nd ed. - New York Wiley Eastern Ltd 2002. - xx, 625 pages ; - Wiley series in probability and mathematical statistics. .
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.
9780852267530 0852267533
Statistical Inference
Mathematical statistics.
Probabilities
519.54 / RAO