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ON THE EXISTENCE OF MINIMUM CONTRAST

ESTIMATES IN BINARY RESPONSE MODEL

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

^{1} *Department of Information Science, Shimane University, 1060 Nishikawatsu-cho,*

Matsue, Shimane 690, Japan

^{2} *Graduate 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.

**Source**
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