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Error Variance Estimation in Ultrahigh-Dimensional Additive Models

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  • Zhao Chen
  • Jianqing Fan
  • Runze Li

Abstract

Error variance estimation plays an important role in statistical inference for high-dimensional regression models. This article concerns with error variance estimation in high-dimensional sparse additive model. We study the asymptotic behavior of the traditional mean squared errors, the naive estimate of error variance, and show that it may significantly underestimate the error variance due to spurious correlations that are even higher in nonparametric models than linear models. We further propose an accurate estimate for error variance in ultrahigh-dimensional sparse additive model by effectively integrating sure independence screening and refitted cross-validation techniques. The root n consistency and the asymptotic normality of the resulting estimate are established. We conduct Monte Carlo simulation study to examine the finite sample performance of the newly proposed estimate. A real data example is used to illustrate the proposed methodology. Supplementary materials for this article are available online.

Suggested Citation

  • Zhao Chen & Jianqing Fan & Runze Li, 2018. "Error Variance Estimation in Ultrahigh-Dimensional Additive Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(521), pages 315-327, January.
  • Handle: RePEc:taf:jnlasa:v:113:y:2018:i:521:p:315-327
    DOI: 10.1080/01621459.2016.1251440
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    Cited by:

    1. Wang, Jia & Cai, Xizhen & Li, Runze, 2021. "Variable selection for partially linear models via Bayesian subset modeling with diffusing prior," Journal of Multivariate Analysis, Elsevier, vol. 183(C).
    2. Xiaochao Xia & Hao Ming, 2022. "A Flexibly Conditional Screening Approach via a Nonparametric Quantile Partial Correlation," Mathematics, MDPI, vol. 10(24), pages 1-32, December.
    3. Sayanti Guha Majumdar & Anil Rai & Dwijesh Chandra Mishra, 2023. "Estimation of Error Variance in Genomic Selection for Ultrahigh Dimensional Data," Agriculture, MDPI, vol. 13(4), pages 1-16, April.
    4. Congran Yu & Wenwen Guo & Xinyuan Song & Hengjian Cui, 2023. "Feature screening with latent responses," Biometrics, The International Biometric Society, vol. 79(2), pages 878-890, June.
    5. Wang, Luheng & Chen, Zhao & Wang, Christina Dan & Li, Runze, 2020. "Ultrahigh dimensional precision matrix estimation via refitted cross validation," Journal of Econometrics, Elsevier, vol. 215(1), pages 118-130.
    6. Zhou, Jia & Li, Yang & Zheng, Zemin & Li, Daoji, 2022. "Reproducible learning in large-scale graphical models," Journal of Multivariate Analysis, Elsevier, vol. 189(C).

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