Sankhya: The Indian Journal of Statistics

2003, Volume 65, Pt. 2, 440-463

Strong Consistency Of Minimum Contrast Estimators With Applications

By

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.

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