For the extreme-maximum-value distribution model, we show that maximum likelihood estimates of regression parameter vector is asymptotically existence and strongly consistent under mild conditions

Compound-sequential logit models are extensions of the ordinary logistic regression model, which are designed for complex ordinal outcomes commonly seen in practice. In this paper, we prove strong consistency of the maximum likelihood estimator (MLE) of the regression parameter vector under some mild conditions. We relax the boundedness condition of the regressors required in most existing theoretical results, and all conditions are easy to verify.

For the exponential sequential model, we show that maximum likelihood estimator of regression parameter vector is asymptotically existence and strongly consistent under mild conditions

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In this article, for the sequential-cumulative logit model, we show that maximum likelihood estimates of regression parameter vector is asymptotically existence and strongly consistent under mild conditions