"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. 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. Radhakrishna Rao. A Wiley-interscience Publication. This Paperback Edition Is A Reprint Of 1965 Edition Published By Wiley. Includes Bibliographical References And Indexes. Introduction. The use of matrix theory is now widespread in both pure mathematics and the physical and the social sciences.
