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Pursuit of dynamic structure in quantile additive models with longitudinal data

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  • Cui, Xia
  • Zhao, Weihua
  • Lian, Heng
  • Liang, Hua

Abstract

We consider quantile additive models with dynamic (time-varying) component functions. We allow some of the component functions to be non-dynamic, and show, as expected but technically nontrivially, that estimators of the non-dynamic functions have a faster convergence rate. A penalization-based method, called dynamic structure pursuit, is proposed to automatically identify these non-dynamic functions. Finally, in the sparse setting, a four-stage estimation procedure is proposed which first identifies the nonzero component functions and then applies the identification strategy of the non-dynamic functions. Theoretical and numerical results are provided to illustrate the performance of the estimators.

Suggested Citation

  • Cui, Xia & Zhao, Weihua & Lian, Heng & Liang, Hua, 2019. "Pursuit of dynamic structure in quantile additive models with longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 130(C), pages 42-60.
    • Handle: RePEc:eee:csdana:v:130:y:2019:i:c:p:42-60
    DOI: 10.1016/j.csda.2018.08.017
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