ON THE EXISTENCE OF MINIMUM CONTRAST ESTIMATES IN BINARY RESPONSE MODEL

TADASHI NAKAMURA^{1} AND CHAE-SHIN LEE^{2}

1Department of Information Science, Shimane University, 1060 Nishikawatsu-cho,

Matsue, Shimane 690, Japan 2Graduate School of Natural Science and Technology, Okayama University, 1-1-1 Tsushima-Naka, Okayama 700, Japan

(Received August 8, 1991; revised November 11, 1992)

Abstract. When random samples are drawn from a 3-parameter distribution with a shifted origin and the observations corresponding to each sample are binary, criteria for the existence of minimum contrast estimates are given. These criteria can be drived by a method, called the probability contents boundary analysis. The probabilities of the existence of maximum likelihood estimates and least squares estimates are evaluated, by simulation with 1000 replications, in the case where the underlying distribution is a 3-parameter lognormal distribution or a 3-parameter loglogistic distribution.

Key words and phrases: Binary response data, biological assay, dose response curve model, minimum contrast estimate, maximum likelihood estimate, least squares estimate, three-parameter distribution, slowly varying function.