method of moments
(1.4 hours to learn)
Summary
The method of moments is a simple method for estimating the parameters of a probability distribution from data. The parameters are chosen so that the model moments match the empirical moments.
Context
This concept has the prerequisites:
- expectation and variance (The method of moments requires estimating moments.)
Goals
- Understand what the method of moments estimator is and how to compute it for simple parametric models.
Core resources (read/watch one of the following)
-Paid-
→ Mathematical Statistics and Data Analysis
An undergraduate statistics textbook.
Location:
Section 8.4, "The method of moments," pages 260-267
→ All of Statistics
A very concise introductory statistics textbook.
Location:
Section 9.2, "The method of moments," pages 120-122
Supplemental resources (the following are optional, but you may find them useful)
-Paid-
→ Probability and Statistics
An introductory textbook on probability theory and statistics.
Location:
Section 7.6, "Properties of maximum likelihood estimators," subsection "Method of moments," pages 430-432
See also
- Some other parameter estimation methods include: In exponential families families, the maximum likelihood solution [is equivalent](maximum_likelihood_in_exponential_families) to moment matching.