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Biometrika 1998 85(4):954-959; doi:10.1093/biomet/85.4.954
© 1998 by Biometrika Trust
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MISCELLANEA

Multiple roots in general estimating equations

C. C. HEYDE and R. MORTON

School of Mathematical Sciences, Australian National University Canberra, ACT 0200, Australiachris.heyde{at}maths.anu.edu.au
CSIRO Mathematical and Information Sciences Canberra, ACT 2601, Australiamorton{at}cbr.dit.csiro.au

This paper is concerned with simple methods for picking the correct root of a general estimating equation in the case of multiple roots. The use of methods based on (i) asymptotics, (ii) analogues of empirical information and (iii) goodness-of-fit type criteria are advocated, and examples are provided to illustrate their use. It is argued that there is no need to introduce approximate likelihood-ratio or deviance-based methods.

Key Words: Approximate likelihood ratio • Deviance • Estimating equation • Goodness of fit • Multiple roots • Quasilikelihood


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