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Parametric modeling of quantile regression coefficient functions

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  • Paolo Frumento
  • Matteo Bottai

Abstract

type="main" xml:lang="en"> Estimating the conditional quantiles of outcome variables of interest is frequent in many research areas, and quantile regression is foremost among the utilized methods. The coefficients of a quantile regression model depend on the order of the quantile being estimated. For example, the coefficients for the median are generally different from those of the 10th centile. In this article, we describe an approach to modeling the regression coefficients as parametric functions of the order of the quantile. This approach may have advantages in terms of parsimony, efficiency, and may expand the potential of statistical modeling. Goodness-of-fit measures and testing procedures are discussed, and the results of a simulation study are presented. We apply the method to analyze the data that motivated this work. The described method is implemented in the qrcm R package.

Suggested Citation

  • Paolo Frumento & Matteo Bottai, 2016. "Parametric modeling of quantile regression coefficient functions," Biometrics, The International Biometric Society, vol. 72(1), pages 74-84, March.
    • Handle: RePEc:bla:biomet:v:72:y:2016:i:1:p:74-84
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    Cited by:

    1. Cheng Peng & Stanislav Uryasev, 2023. "Factor Model of Mixtures," Papers 2301.13843, arXiv.org, revised Mar 2023.
    2. Hao, Meiling & Lin, Yuanyuan & Shen, Guohao & Su, Wen, 2023. "Nonparametric inference on smoothed quantile regression process," Computational Statistics & Data Analysis, Elsevier, vol. 179(C).
    3. Firpo, Sergio & Galvao, Antonio F. & Pinto, Cristine & Poirier, Alexandre & Sanroman, Graciela, 2022. "GMM quantile regression," Journal of Econometrics, Elsevier, vol. 230(2), pages 432-452.
    4. Jingwen Tu & Hu Yang & Chaohui Guo & Jing Lv, 2021. "Model averaging marginal regression for high dimensional conditional quantile prediction," Statistical Papers, Springer, vol. 62(6), pages 2661-2689, December.
    5. Gianluca Sottile & Giada Adelfio, 2019. "Clusters of effects curves in quantile regression models," Computational Statistics, Springer, vol. 34(2), pages 551-569, June.
    6. Liang Yang & Zhengxiao Li & Shengwang Meng, 2020. "Risk Loadings in Classification Ratemaking," Papers 2002.01798, arXiv.org, revised Jan 2022.
    7. Maruotti, Antonello & Petrella, Lea & Sposito, Luca, 2021. "Hidden semi-Markov-switching quantile regression for time series," Computational Statistics & Data Analysis, Elsevier, vol. 159(C).
    8. Paolo Frumento & Nicola Salvati, 2021. "Parametric modeling of quantile regression coefficient functions with count data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(4), pages 1237-1258, October.
    9. Rios-Avila, Fernando & Siles, Leonardo & Canavire Bacarreza, Gustavo J., 2024. "Estimating Quantile Regressions with Multiple Fixed Effects through Method of Moments," IZA Discussion Papers 17262, Institute of Labor Economics (IZA).
    10. Viviana Carcaiso & Leonardo Grilli, 2023. "Quantile regression for count data: jittering versus regression coefficients modelling in the analysis of credits earned by university students after remote teaching," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(4), pages 1061-1082, October.
    11. Paolo Frumento & Nicola Salvati, 2020. "Parametric modelling of M‐quantile regression coefficient functions with application to small area estimation," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(1), pages 229-250, January.
    12. Aleida Cobas-Valdés & Javier Fernández-Macho, 2021. "Gender Dissimilarities in Human Capital Transferability of Cuban Immigrants in the US: A Clustering Quantile Regression Coefficients Approach with Consideration of Implications for Sustainability," Sustainability, MDPI, vol. 13(21), pages 1-12, October.
    13. E. Fusco & R. Benedetti & F. Vidoli, 2023. "Stochastic frontier estimation through parametric modelling of quantile regression coefficients," Empirical Economics, Springer, vol. 64(2), pages 869-896, February.
    14. Sottile, Gianluca & Frumento, Paolo, 2022. "Robust estimation and regression with parametric quantile functions," Computational Statistics & Data Analysis, Elsevier, vol. 171(C).

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