A composite likelihood is a combination of low-dimensional likelihood objects useful in applications where the data have complex structure. Although composite likelihood construction is a crucial aspect influencing both computing and statistical properties of the resulting estimator, currently there does not seem to exist a universal rule to combine low-dimensional likelihood objects that is statistically justified and fast in execution. This paper develops a methodology to select and combine the most informative low-dimensional likelihoods from a large set of candidates while carrying out parameter estimation. The new procedure minimizes the distance between composite likelihood and full likelihood scores subject to a constraint representing the afforded computing cost. The selected composite likelihood is sparse in the sense that it contains a relatively small number of informative sub-likelihoods while the noisy terms are dropped. The resulting estimator is found to have asymptotic variance close to that of the minimum-variance estimator constructed using all the low-dimensional likelihoods.
翻译:复合可能性是数据结构复杂的应用中有用的低维可能性对象的组合。虽然复合可能性构造是影响计算和统计结果估计器的特性的一个关键方面,但目前似乎并不存在将统计上合理和快速执行的低维可能性对象结合起来的普遍规则。本文开发了一种方法,在进行参数估计时,从大量候选人中选择和综合最丰富的低维可能性。新的程序尽量减少复合可能性和受可提供计算成本制约的全概率分数之间的距离。选定的复合可能性很少,因为它包含数量相对较少的信息次相似性,而噪音的术语则被删除。结果的估计值与利用所有低维可能性构建的最低差异值相近。