A randomized pairwise likelihood method for complex statistical inferences

Gildas Mazo (1, 2) , Dimitris Karlis (3) , Andrea Rau (2, 4, 5, 6, 7, 8)

1 MaIAGE - Mathématiques et Informatique Appliquées du Génome à l'Environnement [Jouy-En-Josas]
2 Université Paris-Saclay
3 AUEB - Athens University of Economics and Business
4 GABI - Génétique Animale et Biologie Intégrative
5 AgroParisTech
6 BioEcoAgro - UMR transfrontalière INRAE 1158
7 Université de Lille
8 Université de Liège

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, such as multivariate count data. Although pairwise likelihood methods represent a use- ful solution to perform inference for intractable likelihoods, several computational challenges remain. The pairwise likelihood function still requires the computation of a sum over all pairs of variables and all observations, which may be prohibitive in high dimensions. Moreover, it may be difficult to calculate confidence intervals of the resulting estimators, as they involve summing all pairs of pairs and all of the four-dimensional marginals. To alleviate these issues, we consider a randomized pairwise likelihood approach, where only summands randomly sampled across ob- servations and pairs are used for the estimation. In addition to the usual tradeoff between statistical and computational efficiency, it is shown that, under a condition on the sampling parameter, this two-way random sampling mechanism makes the individual bivariate likelihood scores become asymptotically independent, allowing more computationally efficient confidence intervals to be constructed. The proposed approach is illustrated in tandem with copula-based models for multivariate count data in simulations, and in real data from a transcriptome study.

Mots clés: pairwise likelihood; composite likelihood; randomization; confidence intervals; mutivariate count data; computational challenges

Domaines: Statistiques [math.ST]

Gildas Mazo, Dimitris Karlis, Andrea Rau. A randomized pairwise likelihood method for complex statistical inferences. Journal of the American Statistical Association, 2023, ⟨10.1080/01621459.2023.2257367⟩. ⟨hal-03126620v5⟩