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Biometrika 1976 63(1):199-201; doi:10.1093/biomet/63.1.199
© 1976 by Biometrika Trust
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Miscellanea

A note on the determination of the nature of turning points of likelihoods

N. R. COX*

Department of Mathematics, Imperial College London
* Now at Ruakura Agricultural Research Centre, Biometrics Section, Hamilton, New Zealand.

This note describes an analytical technique for determining whether a solution of the likelihood equations is a maximum, a minimum or a saddle point. The method is based on pivotal reduction as parameters are sequentially eliminated from the equations. As an example a special case of tho linear functional relationship problem is discussed.

Key Words: Likelihood function • Numerical optimization • Pivotal reduction • Sequential elimination • Turning point


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