SIMPLE COMPUTER INTENSIVE METHODS FOR ESTIMATING PARAMETERS OF COMPLEX-MODELS

Two computer intensive methods are proposed for quick and dirty estimates of parameters of complex parametric models. Given n i.i.d. observations on a random variable, one may form a feature vector X, representing what seem to be relevant information in the data. By simulation, it is possible to estimate, (i) the covariance matrix of X for a value theta-0 which is thought to be close to the true value of the parameter, and (ii) the derivative of E-theta(X) with respect to theta at theta-0. From this information, simple matrix manipulations yield a locally best unbiased estimate of theta which is linear in X. A variation of this method involves selecting theta-i according to some random or deterministic scheme, simulating X(i) corresponding to theta-i, and regressing theta-i on X(i) to find an estimator linear in X. This second method has a Bayesian interpretation. The calculations for these methods require the ability to simulate data from the model, and to do simple matrix calculations. The results depend in part on the choice of theta-0 which may be based on a relatively crude preliminary estimate of theta or on some prior knowledge. These methods were suggested by an analysis of an astronomical problem involving apparent superluminal motion, and these and other methods are examined with that problem as the illustrative example.