The heuristic approach in finding initial values for minimum density power divergence estimators

It is well known that in the presence of outliers the maximum likelihood estimates are very unstable. In these situations, an alternative is resorting to the estimators based on the minimum density power divergence criterion for which feasible, computationally closed-form expressions can be derived, so that solutions can be achieved by any standard nonlinear optimization code. But since the function to be minimized is often ill-behaved, the convergence of the algorithm to optimal solutions strongly depends on the choice of the configuration of the initial values. A new procedure based on a heuristic local search approach is introduced in order to survey the parameters space and hence obtaining an accurate set of starting guesses for the gradient-method minimization routine.