Limit theorems for maximum likelihood estimators in the Curie-Weiss-Potts model
The Curie-Weiss-Potts model, generalizing the Curie-Weiss model of ferromagnetism, is considered. The maximum likelihood estimators (MLE) of the parameter \(\beta\) (the inverse temperature) and \(h\) (the external magnetic field) are considered The asymptotic behavior of MLE of a) \(\beta\) when \(h=0\), b) \(h\) when \(\beta\) is known and the true value of \(h\) is \(0\), is established. For \(h=0\), three different types of limiting distributions depending on the critical inverse temperature \(\beta_ c>0\) are obtained.
scientific article; zbMATH DE number 56968
scientific article