When Composite Likelihood meets Stochastic Approximation
提出一种基于随机优化的复合似然估计方法，解决大量似然分量和大样本下的计算难题，证明估计量渐近正态，并通过模拟和心理健康调查数据展示有效性。
A composite likelihood is an inference function derived by multiplying a set of likelihood components. This approach provides a flexible framework for drawing inferences when the likelihood function of a statistical model is computationally intractable. While composite likelihood has computational advantages, it can still be demanding when dealing with numerous likelihood components and a large sample size. This paper tackles this challenge by employing an approximation of the conventional composite likelihood estimator based on a stochastic optimization procedure. This novel estimator is shown to be asymptotically normally distributed around the true parameter. In particular, based on the relative divergent rate of the sample size and the number of iterations of the optimization, the variance of the limiting distribution is shown to compound for two sources of uncertainty: the sampling variability of the data and the optimization noise, with the latter depending on the sampling distribution used to construct the stochastic gradients. The advantages of the proposed framework are illustrated through simulation studies on two working examples: an Ising model for binary data and a gamma frailty model for count data. Finally, a real-data application is presented, showing its effectiveness in a large-scale mental health survey.