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Review - 5703

青鸾惊鸿 2022-02-08 阅读 70
概率论

Content

Lecture 1 Intro

  • LLN (Law of large numbers)
  • CLT (Central Limit Theorem)
  • CMT (Continuous Mapping Theorem)
  • ST (Slutsky’s Theorem)
  • Delta Method

Lecture 2 Estimation

Estimation:

  • unbiased
  • consistent
  • Accuracy of an estimator: M S E = V a r ( θ ^ ) + b i a s ( θ , θ ^ ) = V a r ( θ ^ ) + [ E ( θ ^ ) − θ ) ] 2 MSE = Var(\hat{\theta}) + bias(\theta, \hat{\theta}) = Var(\hat{\theta}) + [E(\hat{\theta}) - \theta)]^2 MSE=Var(θ^)+bias(θ,θ^)=Var(θ^)+[E(θ^)θ)]2
  • Relative efficiency

Two estimation methods

Method of Moments

  • Theorem

Maximum Likelihood Estimator

  • Fisher information
  • Theorem (consistent, unbiased)

Optimality in estimation

  • Cramer-Rao lower bound

Lecture 3 Confidence intervals and hypothesis testing

举报

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