The Annals of Statistics

Estimation for the Nonlinear Functional Relationship

Yasuo Amemiya and Wayne A. Fuller

Full-text: Open access

Abstract

Estimation of the parameters of the nonlinear functional model with known error covariance matrix is discussed. Asymptotic properties of the maximum likelihood estimator for the implicit functional model are presented. The approximate bias in the maximum likelihood estimator due to the nonlinearity of the relationship is given and a bias-adjusted estimator is suggested. Numerical and theoretical results support the superiority of the bias-adjusted estimator relative to the maximum likelihood estimator.

Article information

Source
Ann. Statist. Volume 16, Number 1 (1988), 147-160.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aos/1176350696

Digital Object Identifier
doi:10.1214/aos/1176350696

Mathematical Reviews number (MathSciNet)
MR924862

Zentralblatt MATH identifier
0669.62046

JSTOR
links.jstor.org

Subjects
Primary: 62J02: General nonlinear regression
Secondary: 62F12: Asymptotic properties of estimators 62H12: Estimation

Keywords
Nonlinear implicit relationship measurement errors asymptotic bias maximum likelihood estimator bias-adjusted estimator

Citation

Amemiya, Yasuo; Fuller, Wayne A. Estimation for the Nonlinear Functional Relationship. Ann. Statist. 16 (1988), no. 1, 147--160. doi:10.1214/aos/1176350696. http://projecteuclid.org/euclid.aos/1176350696.


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