Statistical Inference with Local Optima
研究了多峰似然函数下梯度上升法多次初始化的估计量性质，分析了置信区间覆盖不足及不同检验方法导致的差异，并提出了两样本检验过程。
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.