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March, 1994 Potential Functions and Conservative Estimating Functions
Bing Li, Peter McCullagh
Ann. Statist. 22(1): 340-356 (March, 1994). DOI: 10.1214/aos/1176325372


A quasiscore function, as defined by Wedderburn and by McCullagh, frequently fails to have a symmetric derivative matrix. Such a score function cannot be the gradient of any potential function on the parameter space; that is, there is no "quasilikelihood." Without a likelihood function it is difficult to distinguish good roots from bad roots or to set satisfactory confidence limits. From a different perspective, a potential function seems to be essential in order to give the theory an approximate Bayesian interpretation. The purpose of this paper is to satisfy these needs by developing a method of projecting the true score function onto a class of conservative estimating functions. By construction, a potential function for the projected score exists having many properties of a log-likelihood function.


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Bing Li. Peter McCullagh. "Potential Functions and Conservative Estimating Functions." Ann. Statist. 22 (1) 340 - 356, March, 1994.


Published: March, 1994
First available in Project Euclid: 11 April 2007

zbMATH: 0805.62003
MathSciNet: MR1272087
Digital Object Identifier: 10.1214/aos/1176325372

Primary: 62J12
Secondary: 62A10, 62A15

Rights: Copyright © 1994 Institute of Mathematical Statistics


Vol.22 • No. 1 • March, 1994
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