DISCRETIZED LIKELIHOOD METHODS - ASYMPTOTIC PROPERTIES OF DISCRETIZED LIKELIHOOD ESTIMATORS (DLES)

Suppose that X 1, X 2, ..., X n, ... is a sequence of i.i.d. random variables with a density f(x, θ). Let c n be a maximum order of consistency. We consider a solution {Mathematical expression} of the discretized likelihood equation {Mathematical expression} where a n (θ, r) is chosen so that {Mathematical expression} is asymptotically median unbiased (AMU). Then the solution {Mathematical expression} is called a discretized likelihood estimator (DLE). In this paper it is shown in comparison with DLE that a maximum likelihood estimator (MLE) is second order asymptotically efficient but not third order asymptotically efficient in the regular case. Further it is seen that the asymptotic efficiency (including higher order cases) may be systematically discussed by the discretized likelihood methods. © 1979 Kluwer Academic Publishers.