Efficient parameter estimation and variable selection in partial linear varying coefficient quantile regression model with longitudinal data

Kangning Wang and Xiaofei Sun ()
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Kangning Wang: Shandong Technology and Business University
Xiaofei Sun: Shandong Technology and Business University

Statistical Papers, 2020, vol. 61, issue 3, No 3, 967-995

Abstract: Abstract Efficient estimation and variable selection in partial linear varying coefficient quantile regression model with longitudinal data is concerned in this paper. To improve estimation efficiency in quantile regression, based on B-spline basis approximation for nonparametric parts, we propose a new estimating function, which can incorporate the correlation structure between repeated measures. In order to reduce computational burdens, the induced smoothing method is used. The new method is empirically shown to be much more efficient and robust than the popular generalized estimating equations based methods. Under mild conditions, the asymptotically normal distribution of the estimators for the parametric components and the optimal convergence rate of the estimators for the nonparametric functions are established. Furthermore, to do variable selection, a smooth-threshold estimating equation is proposed, which can use the correlation structure and select the nonparametric and parametric parts simultaneously. Theoretically, the variable selection procedure works beautifully, including consistency in variable selection and oracle property in estimation. Simulation studies and real data analysis are included to show the finite sample performance.

Keywords: Semiparametric model; Longitudinal data; Basis spline; Quantile regression; Variable selection; Oracle property; 62G05; 62E20; 62J02 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s00362-017-0970-0

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