Statistical Inference
Lecture Notes
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\[\operatorname {Var}_{\theta }(T(X))\ \geq \ \frac {[\tau '(\theta )]^2}{I_n(\theta )}\]
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