Statistical Inference with Local Optima
Statistical Inference with Local Optima
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DOI：
10.1080/01621459.2021.2023550
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发表时间：
2018-07
影响因子：
3.7
通讯作者：
Yen-Chi Chen
中科院分区：
文献类型：
--
作者：
Yen-Chi Chen
摘要本文研究了多模态似然函数的梯度上升方法的估计量的统计性质。我们推导出的人口数量，这是这个估计的目标，并研究的性质的置信区间（CI）构造的渐近正态性和自助方法。特别是，我们分析了由于有限数量的随机初始化的覆盖不足。我们还调查了CI反转的似然比检验，得分检验，和Wald检验，我们表明，由此产生的CI可能是非常不同的。我们提出了一个双样本测试程序，即使最大似然估计是棘手的。此外，我们分析了随机初始化下的EM算法的性能，并推导出有限数量的初始化CI的覆盖范围。本文的补充材料可在网上查阅。
Abstract We study the statistical properties of an estimator derived by applying a gradient ascent method with multiple initializations to a multi-modal likelihood function. We derive the population quantity that is the target of this estimator and study the properties of confidence intervals (CIs) constructed from asymptotic normality and the bootstrap approach. In particular, we analyze the coverage deficiency due to finite number of random initializations. We also investigate the CIs by inverting the likelihood ratio test, the score test, and the Wald test, and we show that the resulting CIs may be very different. We propose a two-sample test procedure even when the maximum likelihood estimator is intractable. In addition, we analyze the performance of the EM algorithm under random initializations and derive the coverage of a CI with a finite number of initializations. Supplementary materials for this article are available online.