WJWJ Maths
Statistical Inference
  • PROPERTIES OF STATISTICS
  • Introduction
  • Unbiasedness and Mean Square Error
  • Sufficiency
  • Minimal Sufficiency
  • Completeness
  • The Exponential Family
  • Ancillary Statistics
  • MAXIMUM LIKELIHOOD ESTIMATION
  • Introduction
  • Properties of the Score and Information
  • The Information Inequality
  • Limiting Distributions (Review)
  • Large Sample properties of \(ML\) estimators
  • OTHER ESTIMATION CRITERIA
  • Best Linear Unbiased Estimators
  • Equivariant Estimators
  • Estimating Equations
  • Bayes Estimation
  • HYPOTHESIS TESTS
  • Introduction
  • Uniformly Most Powerful Tests
  • Locally Most Powerful tests
  • Likelihood ratio tests
  • Score and Wald Tests
  • REFERENCES

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Chapter 2
MAXIMUM LIKELIHOOD ESTIMATION

2.1 Introduction
2.2 Properties of the Score and Information
2.2.1 The Multiparameter Score and Information
2.2.2 The Likelihood Equation and its Solution
2.3 The Information Inequality
2.4 Limiting Distributions (Review)
2.5 Large Sample properties of \(ML\) estimators
2.5.1 Consistency and Asymptotic Normality
2.5.2 Pivotal Quantities and Confidence Intervals
2.5.3 The Multiparameter Case

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