7. Asmptotic Sampling Distributions of Maximum Likelihood Estimators (MLE)

Topics, Class Notes and Code Assignments and Recommended Readings
  • Review of likelihood function of parameters
  • Fundamental Concepts
    • Covariance and Covariance matrix
    • Covariance of MLE
      • Score/gradient function
      • Observed Hessian and Fisher information matrices
      • Covariance matrix of MLE
  • Asymptotic Sampling Distribution of MLE
    • Multivariate normal distribution
    • Asymptotic sampling distribution of MLE
  • Implementing with R Functions
    • using R wrapper functions for optimization with caution
  • Notes and code
    • Asymptotic Sampling Distribution of the MLE [HTML]
  • A Slightly Technical Note on the MLE [PDF]
    • Section 1: examples 1, 2, and 11 (optional)
    • Section 4: univariate asymptotic properties
    • Section 5: multivariate asymptotic properties
  • A Big-picture View of R Tools for Optimization: jstatsoft paper [PDF]
  • Suggested R Functions for Optimization
    • General: optim(), nlm(), nlminb()
    • Specialized: optimx()
    • Global: DEoptim()
  • Midterm Exam