Discussion on the paper ‘A review of distributed statistical inference’

Distributed statistical inferences have attracted more and more attention in recent years with the emergence of massive data. We are grateful to the authors for the excellent review of the literature in this active area. Besides the progress mentioned by the authors, we would like to discuss some additional development in this interesting area. Specifically, we focus on the balance of communication cost and the statistical efficiency of divide-and-conquer (DC) type estimators in linear discriminant analysis and hypothesis testing. It is seen that the DC approach has different behaviours in these problems, which is different from that in estimation problems. Furthermore, we discuss some issues on the statistical inferences under restricted communication budgets.