论文标题
最大似然估计了三胞胎样本的比例
Maximum Likelihood Estimation of a Proportion from a Sample of Triplets
论文作者
论文摘要
当估计比例和仅给出三胞胎样本时，应考虑三胞胎中的依赖项。如果不假设三胞胎成功计数的分布以及比例，则是第二和第三参数，即一阶和第二阶的相关性输入模型。我们采用最大似然估计，并通过使用三重态计数是多元分布的，并结合了连续映射定理，从而得出一致性。渐近正态性与三角洲方法进行，从而导致标准误差的闭合表达式。随着应用，我们研究了学龄前儿童从样本到护理学校的龋齿患病率。我们将标准错误与假设在护理学校中错误独立的标准错误进行了比较。值得怀疑的是，设计显着“夸大”标准误差。
When estimating a proportion and only a sample of triplets is given, dependencies within the triplets are to be accounted for. Without assuming a distribution for the success count of the triplet, together with the proportion, as second and third parameter the correlations of 1st and 2nd order enter the model. We apply maximum likelihood estimation, and derive consistency by using that the triplet count is multinomially distributed, combined with the continuous mapping theorem. The asymptotic normality follows with the delta-method, resulting in closed-form expressions for the standard errors. As application we study caries prevalence of pre-school children from a sample to nursing schools. We compare the standard errors with those for assuming erroneously independence within the nursing schools. As to be suspected, the design `inflates' the standard error markedly.
