A CAUTIONARY NOTE ON LIKELIHOOD RATIO TESTS IN MIXTURE MODELS

WILFRIED SEIDEL^{1}, KARL MOSLER^{2} AND MANFRED ALKER^{1}*

1Fachbereich Wirtschafts- und Organisationswissenschaften, Universität der Bundeswehr Hamburg,

D-22039 Hamburg, Germany

2Seminar für Wirtschafts- und Sozialstatistik, Universität zu Köln, D-50923 Köln, Germany

(Received December 1, 1997; revised April 5, 1999)

Abstract. We show that iterative methods for maximizing the likelihood in a mixture of exponentials model depend strongly on their particular implementation. Different starting strategies and stopping rules yield completely different estimators of the parameters. This is demonstrated for the likelihood ratio test of homogeneity against two-component exponential mixtures, when the test statistic is calculated by the EM algorithm.

Key words and phrases: EM algorithm, exponential mixture models, initial values, stopping criteria, maximum likelihood estimation, likelihood ratio test.