If I want to fit a distribution (let's say we can be certain about the type) to observations using maximum-likelihood method, I have many options to express the parameter estimation uncertainty due to scarcity of data, e.g. constructing confidence intervals using (following [Coles, 2001]):
- asymptotic normality [Coles, 2001, Ch. 2.6.4]
- deviance function [Coles, 2001, Ch. 2.6.5]
- profile likelihood [Coles, 2001, Ch. 2.6.6]
According to Coles all of these approaches are applicable
only to maximum-likelihood estimation.
So my question: Is there any method to do similar quantification of parameter estimation uncertainty using method of moments?
Is it possible to derive asymptotic distributions as in case of maximum-likelihood approach?
I think bootstrapping might be used for this purpose, but it is a quite expensive approach. Any advice, reference is greatly appreciated.
S. Coles. 2001. An Introduction to Statistical Modeling of Extreme Values. Springer. ISBN 978-1-4471-3675-0.