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Large-Scale Global and Simultaneous Inference: Estimation and Testing in Very High Dimensions

Author

Listed:
  • T. Tony Cai

    (Department of Statistics, The Wharton School, University of Pennsylvania, Philadelphia, Pennsylvania 19104)

  • Wenguang Sun

    (Department of Data Sciences and Operations, Marshall School of Business, University of Southern California, Los Angeles, California 90089)

Abstract

Due to rapid technological advances, researchers are now able to collect and analyze ever larger data sets. Statistical inference for big data often requires solving thousands or even millions of parallel inference problems simultaneously. This poses significant challenges and calls for new principles, theories, and methodologies. This review provides a selective survey of some recently developed methods and results for large-scale statistical inference, including detection, estimation, and multiple testing. We begin with the global testing problem, where the goal is to detect the existence of sparse signals in a data set, and then move to the problem of estimating the proportion of nonnull effects. Finally, we focus on multiple testing with false discovery rate (FDR) control. The FDR provides a powerful and practical approach to large-scale multiple testing and has been successfully used in a wide range of applications. We discuss several effective data-driven procedures and also present efficient strategies to handle various grouping, hierarchical, and dependency structures in the data.

Suggested Citation

  • T. Tony Cai & Wenguang Sun, 2017. "Large-Scale Global and Simultaneous Inference: Estimation and Testing in Very High Dimensions," Annual Review of Economics, Annual Reviews, vol. 9(1), pages 411-439, September.
    • Handle: RePEc:anr:reveco:v:9:y:2017:p:411-439
    DOI: 10.1146/annurev-economics-063016-104355
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    Citations

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    Cited by:

    1. Alexandre Belloni & Victor Chernozhukov & Denis Chetverikov & Christian Hansen & Kengo Kato, 2018. "High-dimensional econometrics and regularized GMM," CeMMAP working papers CWP35/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Vincent, Kendro & Hsu, Yu-Chin & Lin, Hsiou-Wei, 2021. "Investment styles and the multiple testing of cross-sectional stock return predictability," Journal of Financial Markets, Elsevier, vol. 56(C).

    More about this item

    Keywords

    compound decision problem; dependence; detection boundary; false discovery rate; global inference; multiple testing; null distribution; signal detection; simultaneous inference; sparsity;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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