MAXIMUM LIKELIHOOD ESTIMATION IN THE MULTI-PATH CHANGE-POINT PROBLEM

LAWRENCE JOSEPH^{1} AND DAVID B. WOLFSON^{2}

1Division of Clinical Epidemiology, Department of Medicine, Montreal General Hospital,

1650 Cedar Avenue, Montreal, Quebec, Canada H3G 1A4

2Department of Mathematics and Statistics, Burnside Hall, 805 Sherbrooke Street West, McGill University, Montreal, Quebec, Canada H3A 2K6

(Received November 20, 1991; revised June 19, 1992)

Abstract. Maximum likelihood estimators of the parameters of the distributions before and after the change and the distribution of the time to change in the multi-path change-point problem are derived and shown to be consistent. The maximization of the likelihood can be carried out by using either the EM algorithm or results from mixture distributions. In fact, these two approaches give equivalent algorithms. Simulations to evaluate the performance of the maximum likelihood estimators under practical conditions, and two examples using data on highway fatalities in the United States, and on the health effects of urea formaldehyde foam insulation, are also provided.

Key words and phrases: Change-point, maximum likelihood estimation, EM algorithm, mixture distribution.