Statistical Inference
Lecture Notes
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\[\operatorname {Var}_{\theta }\big (T(X)\big )\ \geq \ \frac {\big [\tau '(\theta )\big ]^2}{I_n(\theta )}\]
TABLE OF CONTENTS
1 PROPERTIES OF STATISTICS
1.1 Introduction
1.2 Unbiasedness and Mean Square Error
1.3 Sufficiency
1.4 Minimal Sufficiency
1.5 Completeness
1.6 The Exponential Family
1.7 Ancillary Statistics
2 MAXIMUM LIKELIHOOD ESTIMATION
2.1 Introduction
2.2 Properties of the Score and Information
2.3 The Information Inequality
2.4 Limiting Distributions (Review)
2.5 Large Sample properties of \(ML\) estimators
3 OTHER ESTIMATION CRITERIA
3.1 Best Linear Unbiased Estimators
3.2 Equivariant Estimators
3.3 Estimating Equations
3.4 Bayes Estimation
4 HYPOTHESIS TESTS
4.1 Introduction
4.2 Uniformly Most Powerful Tests
4.3 Locally Most Powerful tests
4.4 Likelihood ratio tests
4.5 Score and Wald Tests
REFERENCES
REFERENCES
1 PROPERTIES OF STATISTICS
1.1 Introduction
1.2 Unbiasedness and Mean Square Error
1.3 Sufficiency
1.4 Minimal Sufficiency
1.5 Completeness
1.6 The Exponential Family
1.7 Ancillary Statistics
2 MAXIMUM LIKELIHOOD ESTIMATION
2.1 Introduction
2.2 Properties of the Score and Information
2.3 The Information Inequality
2.4 Limiting Distributions (Review)
2.5 Large Sample properties of \(ML\) estimators
3 OTHER ESTIMATION CRITERIA
3.1 Best Linear Unbiased Estimators
3.2 Equivariant Estimators
3.3 Estimating Equations
3.4 Bayes Estimation
4 HYPOTHESIS TESTS
4.1 Introduction
4.2 Uniformly Most Powerful Tests
4.3 Locally Most Powerful tests
4.4 Likelihood ratio tests
4.5 Score and Wald Tests
REFERENCES
REFERENCES