Some Convergence Theory for Iterative Estimation Procedures With an Application to Semiparametric Estimation

We develop general conditions for rates of convergence and convergence in distribution of iterative procedures for estimating finite-dimensional parameters. An asymptotic contraction mapping condition is the centerpiece of the theory. We illustrate some of the results by deriving the limiting distribution of a two-stage iterative estimator of regression parameters in a semiparametric binary response model. Simulation results illustrating the computational benefits of the first-stage iterative estimator are also reported.We thank a co-editor and two referees for comments and criticisms that led to significant improvements in this paper. We also thank Roger Klein for providing us with Gauss code to compute his estimator.