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Ultra high‐dimensional semiparametric longitudinal data analysis

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  • Brittany Green
  • Heng Lian
  • Yan Yu
  • Tianhai Zu

Abstract

As ultra high‐dimensional longitudinal data are becoming ever more apparent in fields such as public health and bioinformatics, developing flexible methods with a sparse model is of high interest. In this setting, the dimension of the covariates can potentially grow exponentially as exp(n1/2) with respect to the number of clusters n. We consider a flexible semiparametric approach, namely, partially linear single‐index models, for ultra high‐dimensional longitudinal data. Most importantly, we allow not only the partially linear covariates but also the single‐index covariates within the unknown flexible function estimated nonparametrically to be ultra high dimensional. Using penalized generalized estimating equations, this approach can capture correlation within subjects, can perform simultaneous variable selection and estimation with a smoothly clipped absolute deviation penalty, and can capture nonlinearity and potentially some interactions among predictors. We establish asymptotic theory for the estimators including the oracle property in ultra high dimension for both the partially linear and nonparametric components, and we present an efficient algorithm to handle the computational challenges. We show the effectiveness of our method and algorithm via a simulation study and a yeast cell cycle gene expression data.

Suggested Citation

  • Brittany Green & Heng Lian & Yan Yu & Tianhai Zu, 2021. "Ultra high‐dimensional semiparametric longitudinal data analysis," Biometrics, The International Biometric Society, vol. 77(3), pages 903-913, September.
    • Handle: RePEc:bla:biomet:v:77:y:2021:i:3:p:903-913
    DOI: 10.1111/biom.13348
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    References listed on IDEAS

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    1. Yu Y. & Ruppert D., 2002. "Penalized Spline Estimation for Partially Linear Single-Index Models," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1042-1054, December.
    2. Johnson, Brent A. & Lin, D.Y. & Zeng, Donglin, 2008. "Penalized Estimating Functions and Variable Selection in Semiparametric Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 672-680, June.
    3. Lan Wang & Jianhui Zhou & Annie Qu, 2012. "Penalized Generalized Estimating Equations for High-Dimensional Longitudinal Data Analysis," Biometrics, The International Biometric Society, vol. 68(2), pages 353-360, June.
    4. Jianqing Fan & Jinchi Lv, 2008. "Sure independence screening for ultrahigh dimensional feature space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 849-911, November.
    5. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    6. Ma, Shujie & Liang, Hua & Tsai, Chih-Ling, 2014. "Partially linear single index models for repeated measurements," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 354-375.
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