Hyperparameter Selection for Subsampling Bootstraps

Massive data analysis becomes increasingly prevalent, subsampling methods like BLB (Bag of Little Bootstraps) serves as powerful tools for assessing the quality of estimators for massive data. However, the performance of the subsampling methods are highly influenced by the selection of tuning parameters ( e.g., the subset size, number of resamples per subset ). In this article we develop a hyperparameter selection methodology, which can be used to select tuning parameters for subsampling methods. Specifically, by a careful theoretical analysis, we find an analytically simple and elegant relationship between the asymptotic efficiency of various subsampling estimators and their hyperparameters. This leads to an optimal choice of the hyperparameters. More specifically, for an arbitrarily specified hyperparameter set, we can improve it to be a new set of hyperparameters with no extra CPU time cost, but the resulting estimator's statistical efficiency can be much improved. Both simulation studies and real data analysis demonstrate the superior advantage of our method.