Linear statistical inference and its applications

所蔵情報QRコード

Linear statistical inference and its applications / C. Radhakrishna Rao

版:: 2nd ed
資料種別:: 電子ブック
出版情報:: Wiley Online Libraｒｙ, 1973
形態:: 1 online resource (xx, 625p.)
シリーズ名:: Wiley series in probability and mathematical statistics ; . Probability and mathematical statistics <BA00019013>
著者名:: Rao, Calyampudi Radhakrishna, 1920- <DA0074887X>
ISBN:: 9780470316436 [0470316438] (: electronic bk)
書誌ID:: TT00015709

子書誌情報

フルテキスト

所蔵情報

書誌詳細

注記:

Includes bibliographies
Print published: New York : Wiley , 1973

主題:

Mathematical statistics

言語:

英語

目次情報:

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 H_o 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 N_p / 8a.3：

Density Function of the Multivariate Normal Distribution / 8a.4：

Estimation of Parameters / 8a.5：

N_p 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：

Basis of a Vector Space / 1a.2：

Linear Equations / 1a.3：

Vector Spaces with an Inner Product / 1a.4：

続きを見る

東工大ブックレビュー

類似資料:

1 図書 Linear statistical inference and its applications Rao, Calyampudi Radhakrishna, 1920- Wiley	7 図書 Robust inference Maddala, G. S., 1933-, Rao, Calyampudi Radhakrishna, 1920- Elsevier
2 図書 Linear statistical inference and its applications Rao, Calyampudi Radhakrishna, 1920- Wiley	8 図書 Statistical methods in biological and medical sciences Rao, Calyampudi Radhakrishna, 1920-, Chakraborty, Ranajit, 1946- North-Holland, Distributors for the U.S.A. and Canada, Elsevier Science
3 図書 Advanced statistical methods in biometric research Rao, Calyampudi Radhakrishna, 1920- Hafner Pub. Co.	9 図書 Order statistics : applications Balakrishnan, N., Rao, Calyampudi Radhakrishna, 1920- Elsevier
4 図書 Generalized inverse of matrices and its applications Rao, Calyampudi Radhakrishna, 1920-, Mitra, Sujit Kumar Wiley	10 図書 Computational statistics Rao, Calyampudi Radhakrishna, 1920- North-Holland
5 図書 Characterization problems in mathematical statistics Kagan, A. M. (Abram Meerovich), Linnik, I︠U︡. V. (I︠U︡riĭ Vladimirovich), 1915-1972, Rao, C. Radhakrishna … Wiley	11 図書 Handbook of statistics Rao, Calyampudi Radhakrishna, 1920- North-Holland, Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co.
6 図書 Signal processing and its applications Bose, N. K. (Nirmal K.), 1940-, Rao, Calyampudi Radhakrishna, 1920- North-Holland	12 図書 Essays on econometrics and planning : presented to Professor P.C Mahalanobis on the occasion of his 70th birthday Rao, Calyampudi Radhakrishna, 1920- Pergamon Press