Multiple roots of the Tobit log-likelihood
证明Tobit对数似然函数在未变换参数空间中出现多重根的可能性远低于以往认知,所需数据条件在随机抽样中无法满足,且实际寻找“第二根”需要远超现有计算机程序的精度。
We show that the occurence of multiple roots of the Tobit log-likelihood function in the untransformed parameter space is not nearly so likely as heretofore accepted. The conditions which must be met for them to occur require data configurations which could not be met in random sampling. Moreover, to find a 'second root' in practice would require computer programs far more accurate than those which currently exist. Similar results are obtained for a number of other limited dependent variable models.