algorithm to analyse very large data sets—such that we can apply longstanding statistical methods without modifying existing procedures and computation facilities—the number of partitions, the size of each partition, and some tuning parameters will soon become follow-up issues. From a statistical perspective, the more important issue will be how to legitimately and effectively merge the individual result from each partition into an informative one. This is an essential issue when we apply such divide-and-conquer thinking, especially when there is a lack of consistency among the partition results.

From a computation perspective, the distributed/parallel computation method is a powerful way of accelerating the computation procedure, when statistical procedures can be ‘parallelized’ without overly modifying their current algorithms. Leveraging the divide-and-conquer concept, many researchers have applied distributed computation methods to statistical hypothesis testing and estimation; one can reference @Chen2012 [@Zhang2015; @Battey2015; @Lu2016], and the references therein. These studies are proposed under fixed sample size scenarios, and there is currently a dearth of research about how to integrate sequential procedures into a distributed computation method. The current study looks to fill this research gap, at least in part.

When analysing a very large data set featuring lengthy variables, the computation issue becomes an 