Extremum estimators and stochastic optimization methods

Submitted in partial fulfillment for the Requirements for the Degree of PhD in Mathematics, in the Speciality of Statistics in the Faculdade de Ciências e Tecnologia

Extremum estimators is one of the broadest class of statistical methods for the obtention of consistent estimates. The Ordinary Least Squares (OLS), the Generalized Method of Moments (GMM) as well as the Maximum Likelihood (ML) methods are all given as solutions to an optimization problem of interest, and thus are particular instances of extremum estimators. One major concern regarding the computation of estimates of this type is related with the convergence features of the method used to assess the optimal solution. In fact, if the method employed can converge to a local solution, the consistency of the extremum estimator is no longer ensured. This thesis is concerned with the application of global stochastic search and optimization methods to the obtention of estimates based on extremum estimators. For such purpose, a stochastic search algorithm, is proposed and shown to be convergent. We provide applications to classical test functions, as well as to a problem of variance component in a mixed linear model.

FCT(Fundação para a Ciência e a Tecnologia)- SFRH/BD/1569/2004