A short note on fitting a single-index model with massive data

Abstract

This paper studies the inference problem of index coefficient in single-index models under massive dataset. Analysis of massive dataset is challenging owing to formidable computational costs or memory requirements. A natural method is the averaging divide-and-conquer approach, which splits data into several blocks, obtains the estimators for each block and then aggregates the estimators via averaging. However, there is a restriction on the number of blocks. To overcome this limitation, this paper proposed a computationally efficient method, which only requires an initial estimator and then successively refines the estimator via multiple rounds of aggregations. The proposed estimator achieves the optimal convergence rate without any restriction on the number of blocks. We present both theoretical analysis and experiments to explore the property of the proposed method.