The Maximum Likelihood, the Minimum Chi-Square and the Nonlinear Weighted Least-Squares Estimator in the General Qualitative Response Model

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Abstract
This article deals with the general qualitative response model involving several polytomous variables. An extension of Berkson's minimum chi-square estimator to this model is defined and shown to be not always asymptotically efficient, and the conditions under which it is so are derived. It is also shown that the nonlinear weighted least squares method proposed by Walker and Duncan [11] is equivalent to the method of scoring.