This course covers the learning outcomes and goals of Maximum Likelihood Estimation (MLE) in statistics. Students will learn to estimate parameters of various distributions using MLE, such as Bernoulli, Binomial, Normal, Multivariate Normal, Gumbel, Gamma, Negative Binomial, Beta, Multinomial, Double Exponential, Inverse Gamma, and Lindley distributions. The course teaches skills including deriving derivatives, calculating MLEs, using R for data generation and estimation, and understanding the Score Function for asymptotic normality. The teaching method involves theoretical explanations, practical examples, and hands-on exercises using R. This course is intended for individuals interested in advanced statistical estimation techniques and data analysis.
Overview
Syllabus
MLE of a Bernoulli Distribution and a Binomial Distribution.
MLE of a Continuous Uniform Distribution.
MLE of a Normal Distribution and a Mixture of Normal Distributions.
Derivative of a Determinant with respect to a Matrix.
Derivative of a Quadratic Form with respect to a Vector.
Derivative of a Trace with respect to a Matrix.
Maximum Likelihood Estimates for a Multivariate Normal Distribution.
The Score Function - Asymptotic Normality.
Kaplan Meier Estimator as an MLE.
MLE for a Wishart Distribution (central).
MLE of a Gumbel Distribution (part 1).
MLE for a Gumbel Distribution (part 2).
MLEs of a Gamma Distribution (part 1).
MLEs of a Gamma Distribution (part 2).
MLE of a Negative Binomial Distribution.
MLEs for a Beta Distribution (part 1).
Method of Moments and MLEs for a Beta Distribution (part 2).
MLE of a Multinomial Distribution.
MLEs of a Double Exponential Distribution.
Using R to Generate Double Exponential Data and Calculate the MLEs.
MLEs of an Inverse Gamma Distribution.
Using R to find the MLEs and Method of Moments estimators for an Inverse Gamma Distribution.
Generating Data and deriving the MLE for a 2 Parameter Lindley Distribution.
Maximum Likelihood Estimators Beta Binomial Distribution.
Using R: Method of Moments and ML estimators for Beta Binomial Distribution.
Taught by
statisticsmatt
