Strong consistency of minimum contrast estimators with applications

Abstract

We prove a strong consistency result for minimum contrast estimators for general regression problems with independent errors using technically transparent proofs. This unifies the study of strong consistency of least squares estimators in nonlinear regression models and maximum likelihood estimators in generalized linear models. We give new examples from nonlinear regression and generalized linear models where strong consistency can be established from our result. We also demonstrate that in many situations our result is significantly close to the best existing results.