8. Exact and Likelihood-based Asymptotic Confidence Intervals

Topics, Class Notes and Code Assignments and Recommended Readings
  • Confidence Intervals: Concepts and Goodness Measures
  • Pivotal Quantity
    • Definition and examples
    • How quantity is used to construct CI
  • Steps for Pivotal Quantity-based CI
  • Exact and CLT-based Asymptotic CIs
    • CIs for normal populations and variances
    • Large sample CI for population means and proportions
  • CI Based on Asymptotic Normality
  • Likelihood Ratio Confidence Intervals
  • Notes and code
  • Some Additional Notes on Likelihood Estimations
  • R Functions for Nonlinear Equations
    • uniroot(): Package base
    • uniroot.all(): package rootSolve
    • nleqslv(): package nleqslv
  • A note for mathematical algorithms for solving nonlinear equations: [Link]
  • Written Assignment
    • Guidelines [HTML]
    • Due:Thursday, 3/24/2026