STABILIZING PROPERTIES OF MAXIMUM PENALIZED LIKELIHOOD ESTIMATION FORADDITIVE POISSON REGRESSION

The extent to which the maximum penalized likelihood estimation (MPLE) approach provides stability (in the form of existence, uniqueness and continuous dependence) for the solution of non-negative linear incomp lete data problems has been analysed in some detail for Gaussian distr ibuted data and a quadratic penalty. Here, the stability provided by M PLE for the not so widely analysed additive Poisson regression problem is studied for the restricted class of problems where the solution an d the right-hand side are positive. Examining this important class of problems allows standard arguments to produce a quite comprehensive pi cture of the nature of the stabilization. The properties of the penalt y, introduced into the MPLE formalism, are investigated with respect t o the stability it induces for the solution of the underlying underdet ermined or fully determined linear system (moment estimator). In addit ion, a data smoothing only interpretation is derived together with err or estimates which relate MPLE solutions to those of the moment estima tor linear system.