Maximum Likelihood Estimation

Overview

Dive deep into the world of Maximum Likelihood Estimation (MLE) with this comprehensive 3.5-hour tutorial. Explore a wide range of probability distributions, including Bernoulli, Binomial, Continuous Uniform, Normal, Multivariate Normal, Wishart, Gumbel, Gamma, Negative Binomial, Beta, Multinomial, Double Exponential, Inverse Gamma, Lindley, and Beta Binomial. Learn essential mathematical techniques such as matrix derivatives, quadratic forms, and trace operations. Discover the Score Function and its asymptotic normality, as well as the Kaplan Meier Estimator. Gain practical experience using R for data generation, MLE calculations, and method of moments estimations. Master the theoretical foundations and practical applications of MLE across various statistical distributions, enhancing your skills in statistical inference and data analysis.

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.