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
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.
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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.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Koenker, R (2004) Quantile regression for longitudinal data | 1.000 | 12 | 6 | 100% |
| 2 | Frumento, P., and Bottai, M (2016) Parametric modeling of quantile regression coefficient functions self | 1.000 | 9 | 5 | 100% |
| 3 | Arellano, M., and Bonhomme, S (2016) Nonlinear panel data estimation via quantile regression | 0.843 | 3 | 3 | 100% |
| 4 | Frumento, P., and Bottai, M (2017) Parametric modeling of quantile regression coefficient functions with censored and truncated data self | 0.843 | 3 | 3 | 100% |
| 5 | Kim, M.O., and Yang, Y (2011) Semiparametric approach to a random effects quantile regression model | 0.843 | 3 | 3 | 100% |
| 6 | Lamarche, C (2010) Robust penalized quantile regression estimation for panel data | 0.843 | 3 | 3 | 100% |
| 7 | Geraci, M., and Bottai, M (2007) Quantile regression for longitudinal data using the asymmetric Laplace distribution self | 0.811 | 4 | 2 | 100% |
| 8 | Fernández-Val, I (2005) Bias correction in panel data models with individual specific parameters | 0.644 | 4 | 1 | 100% |
| 9 | Hahn, J., and Newey, W (2004) Jackknife and analytical bias reduction for nonlinear panel models | 0.644 | 4 | 1 | 100% |
| 10 | Canay, I.A (2011) A simple approach to quantile regression for panel data | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 47 scored citations.