The dramatic growth of big datasets presents a new challenge to data storage and analysis. Data reduction, or subsampling, that extracts useful information from datasets is a crucial step in big-data analysis. We propose an orthogonal subsampling (OSS) approach for big data with a focus on linear regression models. The approach is inspired by the fact that an orthogonal array of two levels provides the best experimental design for linear regression models in the sense that it minimizes the average variance of the estimated parameters and provides the best predictions. The merits of OSS are three-fold: (i) it is easy to implement and fast; (ii) it is suitable for distributed parallel computing and ensures the subsamples selected in different batches have no common data points, and (iii) it outperforms existing methods in minimizing the mean squared errors of the estimated parameters and maximizing the efficiencies of the selected subsamples. Theoretical results and extensive numerical results show that the OSS approach is superior to existing subsampling approaches. It is also more robust to the presence of interactions among covariates, and, when they do exist, OSS provides more precise estimates of the interaction effects than existing methods. The advantages of OSS are also illustrated through analysis of real data.

Lin Wang

Jake Elmstedt

Weng Kee Wong

Hongquan Xu

The Annals of Applied Statistics

统计研究的范围很广，从直接的主题合作到纯数学理论。 IMS 的最新期刊《应用统计年鉴》针对的是该范围内应用一半的论文。每季以印刷和电子形式出版，我们的目标是为应用统计的所有领域提供及时和统一的论坛。

The Annals of Applied Statistics is a journal that covers a wide range of statistical research, from collaborative studies on applied topics to pure mathematical theory. Published quarterly in both print and electronic formats, our goal is to provide a timely and cohesive forum for all areas of applied statistics.

《Annals of Applied Statistics》是一个涵盖广泛统计研究领域的期刊，既包括应用主题的合作研究，也涉及纯数学理论。该期刊每季度以印刷和电子形式出版，旨在为应用统计的各个领域提供一个及时且统一的学术交流平台。

Annals of Applied Statistics

Orthogonal subsampling for big data linear regression

Theoretical results and extensive numerical results show that the OSS approach is superior to existing subsampling approaches and more robust to the presence of interactions among covariates and, when they do exist, OSS provides more precise estimates of the interaction effects than existing methods.

Category	Quartile
数学	4
数学, 统计学与概率论	4

Orthogonal subsampling for big data linear regression

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Journal Info

Category	Quartile
STATISTICS & PROBABILITY	2