Envelope method with ignorable missing data.
Envelope method with ignorable missing data.
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DOI：
10.1214/21-ejs1881
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发表时间：
2021-01
影响因子：
1.1
通讯作者：
Linquan Ma;Lan Liu;Wei Yang
中科院分区：
文献类型：
--
作者：
Linquan Ma;Lan Liu;Wei Yang
包络方法是最近提出的一种用于多元回归中响应降维的方法。然而，当存在缺失数据时，使用完全病例观测的包络方法可能会导致结果的偏差和效率低下。在本文中，我们推广了当预报器和/或响应随机缺失时的包络估计。具体地说，我们将包络结构引入期望最大化(EM)算法。由于包络方法下的参数不是逐点可辨识的，包络方法的EM算法并不简单，需要进行特殊的分解。我们的方法保证比标准EM算法更有效，或者至少和标准EM算法一样有效。此外，我们的方法具有优于全数据最大似然估计的潜力。我们给出了该方法在正态和非正态情况下的渐近性质。在模拟研究和慢性肾功能不全队列(CRIC)研究中的应用中，证实了比标准EM更有效的收益。
Envelope method was recently proposed as a method to reduce the dimension of responses in multivariate regressions. However, when there exists missing data, the envelope method using the complete case observations may lead to biased and inefficient results. In this paper, we generalize the envelope estimation when the predictors and/or the responses are missing at random. Specifically, we incorporate the envelope structure in the expectation-maximization (EM) algorithm. As the parameters under the envelope method are not pointwise identifiable, the EM algorithm for the envelope method was not straightforward and requires a special decomposition. Our method is guaranteed to be more efficient, or at least as efficient as, the standard EM algorithm. Moreover, our method has the potential to outperform the full data MLE. We give asymptotic properties of our method under both normal and non-normal cases. The efficiency gain over the standard EM is confirmed in simulation studies and in an application to the Chronic Renal Insufficiency Cohort (CRIC) study.