Evaluation of Combining Bootstrap with Multiple Imputation Using R on Knights Landing Platform

Abstract

Cloud computing and big data technologies are converging to offer a cost-effective delivery model for cloud-based big data analytics. Though impacts of size and scaling of big data on cloud have been extensively studied, the effects of complexity of underlying analytic methods on cloud performance have received less attention. This paper will develop and evaluate a computationally intensive statistical methodology to perform inference in the presence of both non-Gaussian data and missing data. Two well-established statistical approaches, bootstrap and multiple imputations (MI), will be combined to form the methodology. Bootstrap is a computer-based nonparametric resampling procedure that involves randomly selecting data many thousands of times to construct an empirical distribution, which is then used to construct confidence intervals for significance tests. This statistical technique enables scientists who conduct studies on data with known non-normality to obtain higher quality significance tests than is possible with a traditional asymptotic, normal-theory based significance test. However, the bootstrapping procedure only works when no data are missing or the data are missing completely at random (MCAR). Missing data can lead to biased estimates when the MCAR assumption is violated. It is unclear how to best implement a bootstrapping procedure in the presence of missing data. The proposed methods will provide guidelines and procedures that will enable researchers to use the technique in all areas of health, behavior and developmental science in which a study has missing data and cannot rely on parametric inference. Either bootstrapping or MI can be computationally expensive, and combining these two can lead to further computation costs in the cloud. Using carefully constructed simulation examples, we demonstrate that it is feasible to implement the proposed methodology in a high performance Knights Landing platform. However, the computation costs are substantial even with small data size. Further studies are needed to study the effects of optimizing the implementation and its performance with big data.