THE CUMULANT GENERATING FUNCTION ESTIMATION METHOD - IMPLEMENTATION AND ASYMPTOTIC EFFICIENCY

This paper deals with the use of the empirical cumulant generating fun ction to consistently estimate the parameters of a distribution from d ata that are independent and identically distributed (i.i.d.). The tec hnique is particularly suited to situations where the density function is unknown or unbounded in parameter space. We prove asymptotic equiv alence of our technique to that of the empirical characteristic functi on and outline a six-step procedure for its implementation. Extensions of the approach to non-i.i.d, situations are considered along with a discussion of suitable applications and a worked example.