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Biometrika 1993 80(4):755-761; doi:10.1093/biomet/80.4.755
© 1993 by Biometrika Trust
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On constrained quasi-likelihood estimation

C. C. HEYDE1 and R. MORTON2

1Statistics Research Section, School of Mathematical Sciences, Australian National University Canberra, ACT 2601, Australia
2Biometrics Unit INRE Canberra, ACT 2601, Australia

For maximum likelihood or least squares parameter estimation subject to a constrained parameter, the standard approach is to use the method of Lagrange multipliers. In this paper it is shown that the same formal procedure applies very generally for constrained quasi-likelihood estimation even though there is ordinarily no objective function to maximize or minimize. This allows for optimal estimation in a wide range of problems where maximum likelihood cannot be used, such as for semiparametric models. The method is very similar to projecting the free estimator or projecting the equations which it solves.

Key Words: Constrained parameter • Estimating function • Lagrange multiplier • Optimal estimation • Quasi-likelihood


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