Quantile regression with varying coefficients

By Mi-Ok Kim. 2007

203 citations recorded by the source corpus.

Quantile regression provides a framework for modeling statistical quantities of interest other than the conditional mean. The regression methodology is well developed for linear models, but less so for nonparametric models. We consider conditional quantiles with varying coefficients and propose a methodology for their estimation and assessment using polynomial splines. The proposed estimators are easy to compute via standard quantile regression algorithms and a stepwise knot selection algorithm. The proposed Rao-score-type test that assesses the model against a linear model is also easy to implement. We provide asymptotic results on the convergence of the estimators and the null distribution of the test statistic. Empirical results are also provided, including an application of the methodology to forced expiratory volume (FEV) data.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/9827ec41bb01dd8fe379c8e8eaeb282dec63ce65

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Citations in the corpus

Estimating Structural Changes in Regression Quantiles (2011, unknown): “From a methodological perspective, this paper is related to the literature of functional coe¢ cient quantile regression models, see Cai and Xu (2008) and Kim (2007).”
A UNIFIED VARIABLE SELECTION APPROACH FOR VARYING COEFFICIENT MODELS (2012, methodology): “In the last decade, many estimation and hypothesis testing methods have been developed for VC models; see for example Wu and Chiang (2000), Huang, Wu, and Zhou (2002) and Kim (2007).”
An Approach to Multivariate Covariate-Dependent Quantile Contours With Application to Bivariate Conditional Growth Charts (2008, methodology): “If we approximate all of the coefficient functions by splines, then models (6) and (7) are known as varying-coefficient quantile regression models; these have been studied by Kim (2007) and Cai and Xu (2007).”
A quantile correlated random coefficients panel data model (2016, methodology): “The integral in (37) can be calculated exactly since β̂p(u; xl) is piecewise linear for each xl with finitely many pieces.”
Quantile regression in partially linear varying coefficient models (2009, methodology): “Focusing on a varying coefficient model, Kim [15] implemented a similar inference procedure for testing the hypothesis that all of the varying coefficients are constant.”
Inference for single-index quantile regression models with profile optimization (2016, background): “Kim (2007) and Wang, Zhu and Zhou (2009) considered varying coefficient models.”
Varying Coefficient Regression Models: A Review and New Developments (2015, background): “Sieve estimators for the quantile specification were considered in Kim (2007).”
Semiparametric quantile regression estimation in dynamic models with partially varying coefficients (2012, background): “Finally, if there is no Xt1 in (2), then model (2) becomes the varying coefficient quantile regression model qτ (Ut, Xt2) = ατ (Ut) T Xt2 (3) studied by Honda (2004) and Kim (2007) for iid data and Cai and Xu (2008) for time series contexts.”