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STAT 450: Statistical Theory

Course outline:

• Distribution Theory.
  • Basic concepts of probability.

  • Distributions

  • Expectation and moments

  • Moment generating functions.

  • Distribution of transformations

• Point estimation
  • Maximum likelihood estimation.

  • Method of moments.

  • Optimality Theory.

  • Bias, mean squared error.

  • Sufficiency.

  • Uniform Minimum Variance (UMV) Unbiased Estimators.

• Hypothesis Testing
  • Neyman Pearson optimality theory.

  • Most Powerful, Uniformly Most Powerful, Unbiased tests.

• Confidence sets
  • Pivots

  • Associated Hypothesis Tests

  • Inversion of hypothesis tests to get confidence sets.

• Decision Theory.