Abstract:
A maximum likelihood (ML) estimation procedure is developed to find the
mean of the exponential family subject to the constraints g(μ) = 0, where
g is a vector valued function of the mean μ, satisfying the usual regularity
constraints. This result forms the basis of an iterative procedure whereby
the ML estimates of the mean values of a particular model are found. The
constraints on the mean vector may be linear or non-linear. The application
of the procedure provides a very :flexible method for modelling data either
directly in terms of certain constraints or in terms of the implied constraints
of the appropriate model. The approach accommodates any choice of model
assuming any predetermined distribution of the error terms, provided that the
covariance matrix of the error terms can be computed.
