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Partially linear single index models for repeated measurements

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  • Ma, Shujie
  • Liang, Hua
  • Tsai, Chih-Ling

Abstract

In this article, we study the estimations of partially linear single-index models (PLSiM) with repeated measurements. Specifically, we approximate the nonparametric function by the polynomial spline, and then employ the quadratic inference function (QIF) together with profile principle to derive the QIF-based estimators for the linear coefficients. The asymptotic normality of the resulting linear coefficient estimators and the optimal convergence rate of the nonparametric function estimate are established. In addition, we employ a penalized procedure to simultaneously select significant variables and estimate unknown parameters. The resulting penalized QIF estimators are shown to have the oracle property, and Monte Carlo studies support this finding. An empirical example is also presented to illustrate the usefulness of penalized estimators.

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  • 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.
    • Handle: RePEc:eee:jmvana:v:130:y:2014:i:c:p:354-375
    DOI: 10.1016/j.jmva.2014.06.011
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    2. 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.
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    5. Zhao, Weihua & Lian, Heng & Zhang, Riquan & Lai, Peng, 2016. "Estimation and variable selection for proportional response data with partially linear single-index models," Computational Statistics & Data Analysis, Elsevier, vol. 96(C), pages 40-56.

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