Quantile regression in partially linear varying coefficient models

By Huixia Judy Wang, Zhongyi Zhu, Jianhui Zhou. 2009

292 citations recorded by the source corpus.

Semiparametric models are often considered for analyzing longitudinal data for a good balance between flexibility and parsimony. In this paper, we study a class of marginal partially linear quantile models with possibly varying coefficients. The functional coefficients are estimated by basis function approximations. The estimation procedure is easy to implement, and it requires no specification of the error distributions. The asymptotic properties of the proposed estimators are established for the varying coefficients as well as for the constant coefficients. We develop rank score tests for hypotheses on the coefficients, including the hypotheses on the constancy of a subset of the varying coefficients. Hypothesis testing of this type is theoretically challenging, as the dimensions of the parameter spaces under both the null and the alternative hypotheses are growing with the sample size. We assess the finite sample performance of the proposed method by Monte Carlo simulation studies, and demonstrate its value by the analysis of an AIDS data set, where the modeling of quantiles provides more comprehensive information than the usual least squares approach.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/1836356f25a682f2500db099d82e9e8b48e203c8

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Citations in the corpus

Varying Coefficient Regression Models: A Review and New Developments (2015, background): “Extensions of these results were obtained by Wang et al. (2009), where a partially linear varying coefficient model was considered.”
A Mallows-Type Model Averaging Estimator for the Varying-Coefficient Partially Linear Model (2018, background): “Using Lemma A.2, Equation (10), Conditions (C.2), (C.6), and (C.8), Chebyshev’s inequality, and Theorem 2 of Whittle (1960), we can obtain, for any δ > 0, that P( 1 > δ|X,Z, ) = op(1).”
Valid Post-Selection Inference in High-Dimensional Approximately Sparse Quantile Regression Models (2013, background): “…prices (Hoshino 2014), to estimate the effects of smoking status, age and pre-HIV infection CD4 percentage on different quantiles of the CD4 percentage population (Wang, Zhu, and Zhou 2009), to estimate the effect of the explanatory variables on ragweed (Jiang 2015), among many others applications.”
ADAPTIVE SEMI-VARYING COEFFICIENT MODEL SELECTION (2012, background): “…(Fan and Zhang (1999); Cai, Fan, and Li (2000); Fan and Zhang (2000a,b); Huang, Wu, and Zhou (2002, 2004); Fan and Huang (2005); Fan and Zhang (2008); Wang, Li, and Huang (2008); Wang and Xia (2009); Wang, Zhu, and Zhou (2009) and references therein) have considered the estimation of the model.”
A UNIFIED VARIABLE SELECTION APPROACH FOR VARYING COEFFICIENT MODELS (2012, methodology): “By Lemmas 1 and 2 in Wang, Zhu, and Zhou (2009), ζ̂∗1 is asymptotically normal distributed with variance-covariance matrix Is−ν .”
Robust and efficient variable selection for semiparametric partially linear varying coefficient model based on modal regression (2013, methodology): “For example, Li et al. (2002) introduced a local least-square method with a kernel weight function for SPLVCM; Zhang et al. (2002) studied SPLVCM based on local polynomial method (Fan and Gijbels 1996); Lu (2008) discussed the SPLVCM in the framework of generalized linear model based on two step est”