半参数对数双线性比值比模型中比值比参数估计的渐近协方差阵
The Asymptotic Covariance Matrix of the Odds Ratio Parameter Estimator in Semiparametric Log-bilinear Odds Ratio Models
摘要：
两个随机变量之间的关联往往是统计研究中的主要兴趣。本文考虑了随机向量X和Y之间的半参数组合模型，该模型的边缘分布是任意的。鉴于比值比函数包含了关于关联的全部信息，重点是双线性对数比值比模型，特别是比值比参数向量θ。θ的最大似然估计量θ^的协方差结构对于渐近推断是非常重要的。为此，不同的表示的估计协方差阵的条件和无条件的抽样方案和不同的渐近方法，取决于是否X和/或Y有有限或任意的支持。主要结果是θ^的估计渐近协方差阵相对于所有上述方法的不变性。作为应用，我们计算了关于θ的线性假设检验的渐近功效-重点是logistic和线性回归模型-这允许确定必要的样本量以实现所需功效。
英文摘要：
The association between two random variables is often of primary interest in statistical research. In this paper semiparametric models for the association between random vectors X and Y are considered which leave the marginal distributions arbitrary. Given that the odds ratio function comprises the whole information about the association the focus is on bilinear log-odds ratio models and in particular on the odds ratio parameter vector θ. The covariance structure of the maximum likelihood estimator θ^ of θ is of major importance for asymptotic inference. To this end different representations of the estimated covariance matrix are derived for conditional and unconditional sampling schemes and different asymptotic approaches depending on whether X and/or Y has finite or arbitrary support. The main result is the invariance of the estimated asymptotic covariance matrix of θ^ with respect to all above approaches. As applications we compute the asymptotic power for tests of linear hypotheses about θ - with emphasis to logistic and linear regression models - which allows to determine the necessary sample size to achieve a wanted power.
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