Introduction to Maximum Likelihood Estimation
Maximum Likelihood Estimation (MLE) is one of the foundational pillars of modern statistics and machine learning. This course provides a rigorous yet intuitive introduction to the theory, mechanics, and practical applications of MLE. Students transition from the foundational concepts of joint probability and likelihood functions to deriving estimators for classical statistical models, understanding asymptotic properties, and implementing estimation algorithms in both R and Python. Topics include the Score function, Fisher Information, the Cramér-Rao Lower Bound, the Wald/LR/Score test trinity, generalized linear models, and numerical optimization via Newton-Raphson and the EM algorithm.
- Level: advanced
- Duration: 10 weeks
- 13 sections
- Price: $19.99
Topics: maximum likelihood estimation, likelihood function, log-likelihood, score function, Fisher information, Cramér-Rao lower bound, asymptotic normality, consistency, asymptotic efficiency, Wald test, likelihood ratio test, score test, Newton-Raphson, EM algorithm, generalized linear models, logit, probit, numerical optimization, profile likelihood, sandwich estimator
What's inside
- Introduction to Maximum Likelihood Estimation
- Chapter 1: Likelihood vs. Probability: A Paradigm Shift
- Chapter 2: The Log-Likelihood Function and Optimization Conditions
- Chapter 3: Analytical MLE for Classical Distributions
- Chapter 4: Multiparameter Estimation and the Normal Distribution
- Chapter 5: Fisher Information and the Cramér-Rao Lower Bound
- Chapter 6: Asymptotic Properties of the MLE
- Chapter 7: Hypothesis Testing — The Trinity of Classical Tests
- Chapter 8: Confidence Intervals, Standard Errors, and Robust Inference
- Chapter 9: Regression Frameworks and Generalized Linear Models
- Chapter 10: Numerical Optimization and the EM Algorithm
- Chapter 11: Course Summary and Further Paths of Study
- Appendix: A Historical Perspective on Maximum Likelihood Estimation