Using Method of Moments with the Bootstrap

See also: Fitting distributions to data, Fitting in ModelRisk, Analyzing and using data, Method of Moments (MoM), Maximum Likelihood Estimates (MLEs), The Bootstrap

If we are attempting to fit a parametric distribution to data, we can obviously use the parametric Bootstrap. For each Bootstrap replication, we can calculate the necessary moments, and then use them to get estimates for the uncertainty about the parameters we are estimating. The Bootstrap/MoM method has the advantage of directly sampling from the joint uncertainty distribution of the parameters, so any correlation is automatically preserved.

However, the MoM is not the most accurate method of estimating a parameter for low number of data points, so this method is preferable for its convenience rather than great accuracy.

 

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