Sankhya: The Indian Journal of Statistics
2003, Volume 65, Pt. 2, 440-463
Strong Consistency Of Minimum Contrast Estimators With Applications
ARUP BOSE and DEBAPRIYA SENGUPTA, Indian Statistical Institute, Kolkata
SUMMARY: 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.
AMS (1991) subject classification. 62F12, 62E20, 62J02, 62J12.
Key words and phrases. Minimum contrast estimator, nonlinear regression, least square estimate, generalized regression, link function, maximum likelihood estimate, law of large numbers, strong consistency.