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1.

図書
図書
1. Linear statistical inference and its applications
[by] C. Radhakrishna Rao
出版情報: New York : Wiley, c1965  xviii, 522 p. ; 24 cm
シリーズ名: Wiley series in probability and mathematical statistics ; . Probability and mathematical statistics
Wiley publications in statistics
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2.

図書
図書
2. Advanced statistical methods in biometric research
[by] C. Radhakrishna Rao
出版情報: Darien, Conn ; New York : Hafner Pub. Co., 1970, [c1952]  xvii, 390 p. ; 24 cm
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3.

図書
図書
3. Linear statistical inference and its applications. 2nd ed
C. Radhakrishna Rao
出版情報: New York : Wiley, 1973  xx, 625 p. ; 24 cm
シリーズ名: Wiley series in probability and mathematical statistics ; . Probability and mathematical statistics
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目次情報: 続きを見る
Algebra of Vectors and Matrices
Probability Theory, Tools and Techniques
Continuous Probability Models
The Theory of Least Squares and Analysis of Variance
Criteria and Methods of Estimation
Large Sample Theory and Methods
Theory of Statistical Inference
Multivariate Analysis
Publications of the Author
Author Index
Subject Index
Algebra of Vectors and Matrices
Probability Theory, Tools and Techniques
Continuous Probability Models
4.

電子ブック
ＥＢ
4. Linear statistical inference and its applications. 2nd ed (: electronic bk)
C. Radhakrishna Rao
出版情報: Wiley Online Libraｒｙ, 1973  1 online resource (xx, 625p.)
シリーズ名: Wiley series in probability and mathematical statistics ; . Probability and mathematical statistics
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目次情報: 続きを見る
Algebra of Vectors and Matrices / Chapter 1：
Vector Spaces
Definition of Vector Spaces and Subspaces / 1a.1：
Basis of a Vector Space / 1a.2：
Linear Equations / 1a.3：
Vector Spaces with an Inner Product / 1a.4：
Complements and Problems
Theory of Matrices and Determinants / lb：
Matrix Operations / 1b.1：
Elementary Matrices and Diagonal Reduction of a Matrix / 1b.2：
Determinants / 1b.3：
Transformations / 1b.4：
Generalized Inverse of a Matrix / 1b.5：
Matrix Representation, of Vector Spaces, Bases, etc / 1b.6：
Idempotent Matrices / 1b.7：
Special Products of Matrices / 1b.8：
Eigenvalues and Reduction of Matrices / 1c：
Classification and Transformation of Quadratic Forms / 1c.1：
Roots of Determinantal Equations / 1c.2：
Canonical Reduction of Matrices / 1c.3：
Projection Operator / 1c.4：
Further Results on g-Inverse / 1c.5：
Restricted Eigenvalue Problem / 1c.6：
Convex Sets in Vector Spaces / 1d：
Definitions / 1d.1：
Separation Theorems for Convex Sets / 1d.2：
Inequalities / 1e：
Cauchy-Schwarz (C-S) Inequality / 1e.1：
Holder?s Inequality / 1e.2：
Hadamard?s Inequality / 1e.3：
Inequalities Involving Moments / 1e.4：
Convex Functions and Jensen?s Inequality / 1e.5：
Inequalities in Information Theory / 1e.6：
Stirling?s Approximation / 1e.7：
Extrema of Quadratic Forms / 1f：
General Results / 1f.1：
Results Involving Eigenvalues and Vectors / 1f.2：
Minimum Trace Problems / 1f.3：
Probability Theory, Tools and Techniques / Chapter 2：
Calculus of Probability / 2a：
The Space of Elementary Events / 2a.l：
The Class of Subsets (Events) / 2a.2：
Probability as a Set Function / 2a.3：
Borel Field (&sigma-field) and Extension of Probability Measure / 2a.4：
Notion of a Random Variable and Distribution Function / 2a.5：
Multidimensional Random Variable / 2a.6：
Conditional Probability and Statistical Independence / 2a.7：
Conditional Distribution of a Random Variable / 2a.8：
Mathematical Expectation and Moments of Random Variables / 2b：
Properties of Mathematical Expectation / 2b.1：
Moments, 2b.3 Conditional Expectation / 2b.2：
Characteristic Function (c.f.) / 2b.4：
Inversion Theorems / 2b.5：
Multivariate Moments / 2b.6：
Limit Theorems / 2c：
Kolmogorov Consistency Theorem / 2c.1：
Convergence of a Sequence of Random Variables / 2c.2：
Law of Large Numbers / 2c.3：
Convergence of a Sequence of Distribution Functions / 2c.4：
Central Limit Theorems / 2c.5：
Sums of Independent Random Variables / 2c.6：
Family of Probability Measures and Problems of Statistics / 2d：
Family of Probability Measures / 2d.1：
The Concept of a Sufficient Statistic / 2d.2：
Characterization of Sufficiency / 2d.3：
Stieltjes and Lebesgue Integrals / Appendix 2A：
Some Important Theorems in Measure Theory and Integration / Appendix 2B：
Invariance / Appendix 2C：
Statistics, Subfields, and Sufficiency / Appendix 2D：
Non-Negative Definiteness of a Characteristic Function / Appendix 2E：
Complements and Problems

Chapter 3: Continuous Probability Models
Univariate Models / 3a：
Normal Distribution / 3a.1：
Gamma Distribution / 3a.2：
Beta Distribution / 3a.3：
Cauchy Distribution / 3a.4：
Student?s t Distribution / 3a.5：
Distributions Describing Equilibrium States in Statistical Mechanics / 3a.6：
Distribution on a Circle / 3a.7：
Sampling Distributions / 3b：
Definitions and Results / 3b.1：
Sum of Squares of Normal Variables / 3b.2：
Joint Distribution of the Sample Mean and Variance / 3b.3：
Distribution of Quadratic Forms / 3b.4：
Three Fundamental Theorems of the least Squares Theory / 3b.5：
The p-Variate Normal Distribution / 3b.6：
The Exponential Family of Distributions / 3b.7：
Symmetric Normal Distribution / 3c：
Definition / 3c.1：
Bivariate Normal Distribution / 3c.2：
General Properties / 3d.1：
The Theory of least Squares and Analysis of Variance / 3d.2：
Theory of least Squares / Linear Estimation)4a：
Gauss-Markoff Setup (Y, Xβ, σ2I) / 4a.1：
Normal Equations and least Squares (l.s.) Estimators / 4a.2：
g-Inverse and a Solution of the Normal Equation / 4a.3：
Variances and Covariances of l.s. Estimators / 4a.4：
Estimation of σ2 / 4a.5：
Other Approaches to the l.s. Theory / Geometric Solution)4a.6：
Explicit Expressions for Correlated Observations / 4a.7：
Some Computational Aspects of the l.s. Theory / 4a.8：
least Squares Estimation with Restrictions on Parameters / 4a.9：
Simultaneous Estimation of Parametric Functions / 4a.10：
least Squares Theory when the Parameters Are Random Variables / 4a.11：
Choice of the Design Matrix / 4a.12：
Tests of Hypotheses and Interval Estimation / 4b：
Single Parametric Function (Inference) / 4b.1：
More than One Parametric Function (Inference) / 4b.2：
Setup with Restrictions / 4b.3：
Problems of a Single Sample / 4c：
The Test Criterion / 4c.1：
Asymmetry of Right and left Femora (Paired Comparison) / 4c.2：
One-Way Classified Data / 4d：
An Example / 4d.1：
Two-Way Classified Data / 4e：
Single Observation in Each Cell / 4e.1：
Multiple but Equal Numbers in Each Cell / 4e.2：
Unequal Numbers in Cells / 4e.3：
A General Model for Two-Way Data and Variance Components / 4f：
A General Model / 4f.1：
Variance Components Model / 4f.2：
Treatment of the General Model / 4f.3：
The Theory and Application of Statistical Regression / 4g：
Concept of Regression (General Theory) / 4g.1：
Measurement of Additional Association / 4g.2：
Prediction of Cranial Capacity (a Practical Example) / 4g.3：
Test for Equality of the Regression Equations / 4g.4：
The Test for an Assigned Regression Function / 4g.5：
Restricted Regression / 4g.6：
The General Problem of least Squares with Two Sets of Parameters / 4h：
Concomitant Variables / 4h.1：
Analysis of Covariance / 4h.2：
An Illustrative Example / 4h.3：
Unified Theory of Linear Estimation / 4i：
A Basic Lemma on Generalized Inverse / 4i.1：
The General Gauss-Markoff Model (GGM) / 4i.2：
The Inverse Partitioned Matrix (IPM) Method / 4i.3：
Untried Theory of Least Squares / 4i.4：
Estimation of Variance Components / 4j：
Minque Theory / 4j.1：
Computation under the Euclidian Norm / 4j.3：
Biased Estimation in Linear Models / 4k：
Best Linear Estimator (BLE) / 4k.1：
Best Linear Minimum Bias Estimation (BLIMBE) Complements and Problems / 4k.2：
Criteria and Methods of Estimation / Chapter 5：
Minimum Variance Unbiased Estimation / 5a：
Minimum Variance Criterion / 5a.1：
Some Fundamental Results on Minimum Variance Estimation / 5a.2：
The Case of Several Parameters / 5a.3：
Fisher?s Information Measure / 5a.4：
An Improvement of Un-biased Estimators / 5a.5：
General Procedures / 5b：
Statement of the General Problem (Bayes Theorem) / 5b.1：
Joint d.f. of (&Teata;, x) Completely Known / 5b.2：
The Law of Equal Ignorance / 5b.3：
Empirical Bayes Estimation Procedures / 5b.4：
Fiducial Probability / 5b.5：
Minimax Principle / 5b.6：
Principle of Invariance / 5b.7：
Criteria of Estimation in Large Samples / 5c：
Consistency / 5c.1：
Efficiency / 5c.2：
Some Methods of Estimation in Large Samples / 5d：
Method of Moments / 5d.1：
Minimum Chi-Square and Associated Methods / 5d.2：
Maximum Likelihood / 5d.3：
Estimation of the Multinomial Distribution / 5e：
Nonparametric Case / 5e.1：
Parametric Case / 5e.2：
Estimation of Parameters in the General Case / 5f：
Assumptions and Notations / 5f.1：
Properties of m.l. Equation Estimators / 5f.2：
The Method of Scoring for the Estimation of Parameters, Complements and Problems / 5g：
Large Sample Theory and Methods / Chapter 6：
Some Basic Results / 6a：
Asymptotic Distribution of Quadratic Functions of Frequencies / 6a.1：
Some Convergence Theorems / 6a.2：
Chi-Square Tests for the Multinomial Distribution / 6b：
Test of Departure from a Simple Hypothesis / 6b.1：
Chi-Square Test for Goodness of Fit / 6b.2：
Test for Deviation in a Single Cell / 6b.3：
Test Whether the Parameters Lie in a Subset / 6b.4：
Some Examples / 6b.5：
Test for Deviations in a Number of Cells / 6b.6：
Tests Relating to Independent Samples from Multinomial Distributions / 6c：
Test of Homogeneity of Parallel Samples / 6c.1：
Contingency Tables / 6c.3：
The Probability of an Observed Configuration and Tests in Large Samples / 6d.1：
Tests of Independence in a Contingency Table / 6d.2：
Tests of Independence in Small Samples / 6d.3：
Some General Classes of Large Sample Tests / 6e：
Notations and Basic Results / 6e.1：
Test of a Simple Hypothesis / 6e.2：
Test of a Composite Hypothesis / 6e.3：
Order Statistics / 6f：
The Empirical Distribution Function / 6f.1：
Asymptotic Distribution of Sample Fractiles / 6f.2：
Transformation of Statistics / 6g：
A General Formula / 6g.1：
Square Root Transformation of the Poisson Variate / 6g.2：
Sin-1 Transformation of the Square Root of the Binomial Proportion / 6g.3：
Tanh-1 Transformation of the Correlation Coefficient / 6g.4：
Standard Errors of Moments and Related Statistics / 6h：
Variances and Covariances of Raw Moments / 6h.1：
Asymptotic Variances and Covariances of Central Moments / 6h.2：
Exact Expressions for Variances and Covariances of Central Moments / 6h.3：
Theory of Statistical Inference / Chapter 7：
Testing of Statistical Hypotheses / 7a：
Statement of the Problem / 7a.1：
Neyman-Pearson Fundamental Lemma and Generalizations / 7a.2：
Simple Ho against Simple H / 7a.3：
Locally Most Powerful Tests / 7a.4：
Testing a Composite Hypothesis / 7a.5：
Fisher-Behrens Problem / 7a.6：
Asymptotic Efficiency of Tests / 7a.7：
Confidence Intervals / 7b：
The General Problem / 7b.1：
A General Method of Constructing a Confidence Set / 7b.2：
Set Estimators for Functions of &Teata; / 7b.3：
Sequential Analysis / 7c：
Wald?s Sequential Probability Ratio Test / 7c.1：
Some Properties of the S.P.R.T / 7c.2：
Efficiency of the S.P.R.T / 7c.3：
An Example of Economy of Sequential Testing / 7c.4：
The Fundamental Identity of Sequential Analysis / 7c.5：
Sequential Estimation / 7c.6：
Sequential Tests with Power One / 7c.7：
Problem of Identification?Decision Theory / 7d：
Randomized and Nonrandomized Decision Rules / 7d.1：
Bayes Solution / 7d.3：
Complete Class of Decision Rules / 7d.4：
Minimax Rule / 7d.5：
Nonparametric Inference / 7e：
Concept of Robustness / 7e.1：
Distribution-Free Methods / 7e.2：
Some Nonparametric Tests / 7e.3：
Principle of Randomization / 7e.4：
Ancillary Information / 7f：
Multivariate Analysis / Chapter 8：
Multivariate Normal Distribution / 8a：
Properties of the Distribution / 8a.1：
Some Characterizations of Np / 8a.3：
Density Function of the Multivariate Normal Distribution / 8a.4：
Estimation of Parameters / 8a.5：
Np as a Distribution with Maximum Entropy / 8a.6：
Wishart Distribution / 8b：
Definition and Notation / 8b.1：
Some Results on Wishart Distribution / 8b.2：
Analysis of Dispersion / 8c：
The Gauss-Markoff Setup for Multiple Measurements / 8c.1：
Tests of Linear Hypotheses, Analysis of Dispersion (A.D.) / 8c.2：
Test for Additional Information / 8c.4：
The Distribution of A / 8c.5：
Test for Dimensionality / Structural Relationship)8c.6：
Analysis of Dispersion with Structural Parameters (Growth Model) / 8c.7：
Some Applications of Multivariate Tests / 8d：
Test for Assigned Mean Values / 8d.1：
Test for a Given Structure of Mean Values / 8d.2：
Test for Differences between Mean Values of Two Populations / 8d.3：
Test for Differences in Mean Values between Several Populations / 8d.4：
Barnard?s Problem of Secular Variations in Skull Characters / 8d.5：
Discriminatory Analysis (Identification) / 8e：
Discriminant Scores for Decision / 8e.1：
Discriminant Analysis in Research Work / 8e.2：
Discrimination between Composite Hypotheses / 8e.3：
Relation between Sets of Variates / 8f：
Canonical Correlations / 8f.1：
Properties of Canonical Variables / 8f.2：
Effective Number of Common Factors / 8f.3：
Factor Analysis / 8f.4：
Orthonormal Basis of a Random Variable / 8g：
The Gram-Schmidt Basis / 8g.1：
Principal Component Analysis / 8g.2：
Publications of the Author
Author Index
Subject Index
Continuous Probability Models
The Theory of Least Squares and Analysis of Variance
Algebra of Vectors and Matrices / Chapter 1：
Vector Spaces
Definition of Vector Spaces and Subspaces / 1a.1：
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