Maximum-likelihood estimators with known incidental parameters

Abstract

Suppose we have a sample of N independent random variables X 1 , …, X N where X i has the distribution F ( X |θ, ø i ). θ is a k -dimensional ‘structural’ parameter (θ (1) , …, θ (k) ), and the ø i are scalar or vector ‘incidental’ parameters in some given space. The X i may be scalar or vector random variables which are either discrete in which case we write f ( X |θ, ø i ) for the probability associated with a given point, or else continuous random variables with a probability density f ( X |θ, ø i ). In either case we sup pose the support of the probability distribution to be fixed. We aim to estimate the true value of θ by maximum-likelihood methods.