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電子ブック
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1. Atomic and laser spectroscopy ((ebook) :)
Alan Corney
出版情報: Oxford : Clarendon, 1977  1 online resource (xvii, 763 p.)
シリーズ名: Oxford classic texts in the physical sciences
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Introduction / 1：
Review of Classical Electrodynamics / 2：
Review of Quantum Mechanics / 3：
The Spontaneous Emission of Radiation / 4：
Selection Rules for Electric Dipole Transitions / 5：
Measurement of Radiative Lifetimes of Atoms and Molecules / 6：
Forbidden Transitions and Metastable Atoms / 7：
The Width and Shape of Spectral Lines / 8：
The Absorption and Stimulated Emission of Radiation / 9：
Radiative Transfer and the Formation of Spectral Lines / 10：
Population Inversion Mechanisms in Gas Lasers / 11：
Resonant Modes of Optical Cavities / 12：
Saturation Characteristics and the Single-Frequency Operation of Gas Lasers / 13：
Turnable Dye Lasers and Atomic Spectroscopy / 14：
The Hanle Effect and the Theory of Resonance Flourescence Experiments / 15：
Optical Double Resonance Experiments / 16：
Optical Pumping Experiments / 17：
The Hyperfine Structure of Atoms and its Investigation by Magnetic Resonance Methods / 18：
Appendix
Introduction / 1：
Review of Classical Electrodynamics / 2：
Review of Quantum Mechanics / 3：
2.

電子ブック
ＥＢ
2. 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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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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