A Large Deviation Result for Parameter Estimators and its Application to Nonlinear Regression Analysis

Elaborating on the work of Ibragimov and Has'minskii (1981) we prove a law of large deviations (LLD) for M-estimators, i.e., those estimators which maximize a functional, continuous in the parameter, of the observations. This LLD is applied, using the results of Petrov (1975), to the problem of...

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Veröffentlicht in:	The Annals of statistics 1987-09, Vol.15 (3), p.1031-1049
Hauptverfasser:	Sieders, Arthur, Dzhaparidze, Kacha
Format:	Artikel
Sprache:	eng
Schlagworte:	60F10 62F12 62J02 Continuous functions Estimators Exact sciences and technology large deviations least-squares M-estimation Mathematical functions Mathematical independent variables Mathematical theorems Mathematics Michaelis-Menten model nonlinear regression Parametric inference Polynomials Probability and statistics Random variables rate of convergence Regression analysis Sciences and techniques of general use Statistical theories Statistics
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Zusammenfassung:	Elaborating on the work of Ibragimov and Has'minskii (1981) we prove a law of large deviations (LLD) for M-estimators, i.e., those estimators which maximize a functional, continuous in the parameter, of the observations. This LLD is applied, using the results of Petrov (1975), to the problem of parametrical nonlinear regression in the situation of discrete time, independent errors and regression functions which are continuous in the parameter. This improves a result of Prakasa Rao (1984).
ISSN:	0090-5364 2168-8966
DOI:	10.1214/aos/1176350491