Statistics and Its Interface

Volume 9 (2016)

Number 4

Special Issue on Statistical and Computational Theory and Methodology for Big Data

Guest Editors: Ming-Hui Chen (University of Connecticut); Radu V. Craiu (University of Toronto); Faming Liang (University of Florida); and Chuanhai Liu (Purdue University)

Smoothing spline ANOVA for super-large samples: scalable computation via rounding parameters

Pages: 433 – 444

DOI: https://dx.doi.org/10.4310/SII.2016.v9.n4.a3

Authors

Nathaniel E. Helwig (Dept. of Psychology and School of Statistics, University of Minnesota (Twin Cities), Minneapolis, Minn., U.S.A.)

Ping Ma (Department of Statistics, University of Georgia, Athens, Ga., U.S.A.)

Abstract

In the current era of big data, researchers routinely collect and analyze data of super-large sample sizes. Data-oriented statistical methods have been developed to extract information from super-large data. Smoothing spline ANOVA (SSANOVA) is a promising approach for extracting information from noisy data; however, the heavy computational cost of SSANOVA hinders its wide application. In this paper, we propose a new algorithm for fitting SSANOVA models to super-large sample data. In this algorithm, we introduce rounding parameters to make the computation scalable. To demonstrate the benefits of the rounding parameters, we present a simulation study and a real data example using electroencephalography data. Our results reveal that (using the rounding parameters) a researcher can fit nonparametric regression models to very large samples within a few seconds using a standard laptop or tablet computer.

Keywords

smoothing spline ANOVA, rounding parameter, scalable algorithm

2010 Mathematics Subject Classification

Primary 62G08, 65D07. Secondary 65D10.

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Published 14 September 2016