Mathematical Statistics Lecture |top| -

The professor will derive the likelihood function ( L(\theta; x) ), not as a probability, but as a measure of evidence. The famous Likelihood Principle is stated: all evidence from an experiment about ( \theta ) is contained in the likelihood function. This is a philosophical earthquake. It implies that the design of an experiment (stopping rules, optional sampling) is irrelevant after the data are collected.

is a classic paper that explains how to define estimators when your data doesn't perfectly follow a standard distribution. The χ2chi squared Test of Goodness of Fit mathematical statistics lecture

Set sample moments equal to population moments and solve for parameters. The professor will derive the likelihood function (