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Parametric Modeling of Quantile Regression Coefficient Functions with Longitudinal Data

Paolo Frumento, Matteo Bottai, Iván Fernández-Val

arXiv 30 May 2020 · Statistics — Methodology · publishedBiometrics (2015) · 61 citations (OpenAlex)

arXiv:2006.00160 · PDF · DOI · OpenAlex · Extracted main text

Abstract

In ordinary quantile regression, quantiles of different order are estimated one at a time. An alternative approach, which is referred to as quantile regression coefficients modeling (QRCM), is to model quantile regression coefficients as parametric functions of the order of the quantile. In this paper, we describe how the QRCM paradigm can be applied to longitudinal data. We introduce a two-level quantile function, in which two different quantile regression models are used to describe the (conditional) distribution of the within-subject response and that of the individual effects. We propose a novel type of penalized fixed-effects estimator, and discuss its advantages over standard methods based on $\ell_1$ and $\ell_2$ penalization. We provide model identifiability conditions, derive asymptotic properties, describe goodness-of-fit measures and model selection criteria, present simulation results, and discuss an application. The proposed method has been implemented in the R package qrcm.

Citation extraction

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appendix boundary found by appendix_titled_section at “Appendix A - Proof of Theorem 1” · 64% of the source is main text. Read the extracted text to check this.

Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Koenker, R (2004) Quantile regression for longitudinal data1.000126100%
2Frumento, P., and Bottai, M (2016) Parametric modeling of quantile regression coefficient functions self1.00095100%
3Arellano, M., and Bonhomme, S (2016) Nonlinear panel data estimation via quantile regression0.84333100%
4Frumento, P., and Bottai, M (2017) Parametric modeling of quantile regression coefficient functions with censored and truncated data self0.84333100%
5Kim, M.O., and Yang, Y (2011) Semiparametric approach to a random effects quantile regression model0.84333100%
6Lamarche, C (2010) Robust penalized quantile regression estimation for panel data0.84333100%
7Geraci, M., and Bottai, M (2007) Quantile regression for longitudinal data using the asymmetric Laplace distribution self0.81142100%
8Fernández-Val, I (2005) Bias correction in panel data models with individual specific parameters0.64441100%
9Hahn, J., and Newey, W (2004) Jackknife and analytical bias reduction for nonlinear panel models0.64441100%
10Canay, I.A (2011) A simple approach to quantile regression for panel data0.64422100%

Showing the top 10 of 47 scored citations.