11. Asymptotic Chi-Square Tests

Topics, Class Notes and Code Assignments and Optional Readings
  • Review of Maximum Likelihood Estimation
  • Formulation of Three Chi-Square Tests
    • Likelihood ratio chi-square test
    • Wald chi-square test
    • Score chi-square test (Rao chi-square test)
  • Practical Examples – Single Parameter Case
    • Implementing all three chi-square tests
  • Practical Examples – Multiparameter Case
    • Likelihood ratio test
    • Wald test
  • Notes and code
  • Optional Reading Assignments
    • Technical note justifying the asymptotic equivalence of the LRT, Wald, and Score tests [PDF]
    • An expository note (non-technical but using matrix notation) [PDF]
    • Ripley's intuitive note on the three chi-square tests [PDF]
    • Pearson chi-square test for goodness-of-fit and independence (cheat sheet) [PDF]
  • Written Assignment
    • Guidelines [HTML]
    • Due:Tuesday, 4/14/2026 at 11:59 PM