论文标题
关于有限混合模型的得分函数的偏差
On the Bias of the Score Function of Finite Mixture Models
论文作者
论文摘要
我们表征了分数函数的无偏见，被视为一类有限混合模型的推理功能。研究的模型代表了有限数量的观测值分层的情况。我们表明，在轻度的规律条件下，估计识别每个组分布的参数的得分函数是公正的。我们还表明，如果一个人在上述方案中引入了混合物，以便对于某些观察结果，只知道它们属于某些群体，而概率不在$ \ {0，1 \} $中，那么得分函数就会有偏见。然后，我们认为，在进一步的轻度规律性下，最大似然估计不一致。上面的结果扩展到包含任意滋扰参数的常规模型，包括半参数模型。
We characterise the unbiasedness of the score function, viewed as an inference function for a class of finite mixture models. The models studied represent the situation where there is a stratification of the observations in a finite number of groups. We show that, under mild regularity conditions, the score function for estimating the parameters identifying each group's distribution is unbiased. We also show that if one introduces a mixture in the scenario described above so that for some observations, it is only known that they belong to some of the groups with a probability not in $\{ 0, 1 \}$, then the score function becomes biased. We argue then that under further mild regularity, the maximum likelihood estimate is not consistent. The results above are extended to regular models containing arbitrary nuisance parameters, including semiparametric models.
