非高斯混合线性模型的部分观测信息与推断
Partially observed information and inference about non-Gaussian mixed linear models
摘要：
在具有非正态数据的混合线性模型中，高斯Fisher信息矩阵称为准信息矩阵（QUIM）。QUIM在估计模型参数估计量的渐近协方差阵（包括方差分量）方面起着重要的作用。传统的信息矩阵估计方法有两种：估计信息矩阵和观测信息矩阵。由于QUIM的解析形式涉及方差分量以外的参数，例如随机效应的三阶矩和四阶矩，因此估计的QUIM不可用。另一方面，由于数据的依赖性和非正态性，所观察到的QUIM是不一致的。我们提出了一个估计的QUIM，部分由一个观察到的形式和部分的估计。我们表明，这种估计是一致的，计算上非常容易操作。该方法用于推导非高斯混合线性模型中包含方差分量的统计假设的大样本检验。通过仿真研究了该检验的有限样本性能，并与适用于非高斯混合线性模型特殊情况的删除组折刀法进行了比较。
英文摘要：
In mixed linear models with nonnormal data, the Gaussian Fisher information matrix is called a quasi-information matrix (QUIM). The QUIM plays an important role in evaluating the asymptotic covariance matrix of the estimators of the model parameters, including the variance components. Traditionally, there are two ways to estimate the information matrix: the estimated information matrix and the observed one. Because the analytic form of the QUIM involves parameters other than the variance components, for example, the third and fourth moments of the random effects, the estimated QUIM is not available. On the other hand, because of the dependence and nonnormality of the data, the observed QUIM is inconsistent. We propose an estimator of the QUIM that consists partially of an observed form and partially of an estimated one. We show that this estimator is consistent and computationally very easy to operate. The method is used to derive large sample tests of statistical hypotheses that involve the variance components in a non-Gaussian mixed linear model. Finite sample performance of the test is studied by simulations and compared with the delete-group jackknife method that applies to a special case of non-Gaussian mixed linear models.
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