A randomized pairwise likelihood method for complex statistical inferences

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Mazo, Gildas | Karlis, Dimitris | Rau, Andrea

Edité par HAL CCSD

Pairwise likelihood methods are commonly used for inference in parametric sta-tistical models in cases where the full likelihood is too complex to be used, suchas multivariate count data. Although pairwise likelihood methods represent a use-ful solution to perform inference for intractable likelihoods, several computationalchallenges remain. The pairwise likelihood function still requires the computationof a sum over all pairs of variables and all observations, which may be prohibitivein high dimensions. Moreover, it may be difficult to calculate confidence intervalsof the resulting estimators, as they involve summing all pairs of pairs and all ofthe four-dimensional marginals. To alleviate these issues, we consider a randomizedpairwise likelihood approach, where only summands randomly sampled across ob-servations and pairs are used for the estimation. In addition to the usual tradeoffbetween statistical and computational efficiency, it is shown that, under a conditionon the sampling parameter, this two-way random sampling mechanism makes theindividual bivariate likelihood scores become asymptotically independent, allowingmore computationally efficient confidence intervals to be constructed. The proposedapproach is illustrated in tandem with copula-based models for multivariate countdata in simulations, and in real data from a transcriptome study.

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