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The expectation-maximization (EM) algorithm is a powerful computationaltechnique for finding the maximum likelihood estimates for parametric modelswhen the data are not fully observed. The EM is best suited for situationswhere the expectation in each E-step and the maximization in each M-step arestraightforward. A difficulty with the implementation of the EM algorithm isthat each E-step requires the integration of the log-likelihood function inclosed form. The explicit integration can be avoided by using what is known asthe Monte Carlo EM (MCEM) algorithm. The MCEM uses a random sample to estimatethe integral at each E-step. However, the problem with the MCEM is that itoften converges to the integral quite slowly and the convergence behavior canalso be unstable, which causes a computational burden. In this paper, wepropose what we refer to as the quantile variant of the EM (QEM) algorithm. Weprove that the proposed QEM method has an accuracy of $O(1/K^2)$ while the MCEMmethod has an accuracy of $O_p(1/\sqrt{K})$. Thus, the proposed QEM methodpossesses faster and more stable convergence properties when compared with theMCEM algorithm. The improved performance is illustrated through the numericalstudies. Several practical examples illustrating its use in interval-censoreddata problems are also provided.

A Quantile Variant of the EM Algorithm and Its Applications to Parameter Estimation with Interval Data