Chapter 1
Properties of Statistics
1.1 Introduction
1.2 Unbiasedness and Mean Square Error
1.2.1 Unbiased Estimators
1.2.2 Mean square error
1.2.3 Uniformly Minimum Variance Unbiased Estimation
1.3 Sufficiency
1.3.1 The Factorisation Criterion
1.4 Minimal Sufficiency
1.5 Completeness
1.5.1 Completeness, Sufficiency and Minimality
1.5.2 Conditioning: Total Expectation and Total Variance
1.5.3 Minimum Variance Unbiased Estimation
1.5.4 The Lehmann–Scheffé Theorem
1.6 The Exponential Family
1.6.1 The Canonical Form
1.6.2 Regular Exponential Families
1.6.3 Completeness in the Exponential Family
1.7 Ancillary Statistics
Further reading
1.2 Unbiasedness and Mean Square Error
1.2.1 Unbiased Estimators
1.2.2 Mean square error
1.2.3 Uniformly Minimum Variance Unbiased Estimation
1.3 Sufficiency
1.3.1 The Factorisation Criterion
1.4 Minimal Sufficiency
1.5 Completeness
1.5.1 Completeness, Sufficiency and Minimality
1.5.2 Conditioning: Total Expectation and Total Variance
1.5.3 Minimum Variance Unbiased Estimation
1.5.4 The Lehmann–Scheffé Theorem
1.6 The Exponential Family
1.6.1 The Canonical Form
1.6.2 Regular Exponential Families
1.6.3 Completeness in the Exponential Family
1.7 Ancillary Statistics
Further reading