Unbiased Simulators for Analytic Functions and Maximum Unbiased Simulated Likelihood Estimation by Gregory

The paper collects some old results and presents some news ones for unbiased estimation of analytic functions of probabilities where the probabilities must be simulated and applies these to Simulated Maximum Likelihood (SML) estimation. The results include unbiased estimation of finite degree polynomials and other analytic functions, unbiased simulation of the score and likelihood, and the asymptotic properties of SML using these simulators. The motivating application is estimation in the mixed logit model. The old results are spread throughout the literature, primarily in the non-parametric and sequential estimation literatures. Moreover, they do not seem known to simulation researchers, much less applied. So they are collected here and presented, in context, with the new results.