Datanomics

I am working on estimating the returns to venture capital using a mixture model. That model should capture the persistent tail events in the returns distribution. Choosing the number of components — how many different “modes” are there –is non-trivial and apparently not solved. Below I list some papers that present their own solutions and test statistics:

Fitting of mixtures with unspecified number of components using cross validation distance estimate

Determining the Number of Component Clusters in the Standard Multivariate Normal Mixture Model Using Model-Selection Criteria.

Testing the number of components in a normal mixture

An entropy criterion for assessing the number of clusters in a mixture model

Unsupervised learning of finite mixture models

Here is a good list of mixture model references with even more papers. The EM algorithm used to generate estimates is found in Dempster, et. al.