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Mixtures of quantile regressions

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  • Wu, Qiang
  • Yao, Weixin

Abstract

A semi-parametric mixture of quantile regressions model is proposed to allow regressions of the conditional quantiles, such as the median, on the covariates without any parametric assumption on the error densities. The median as a measure of center is known to be more robust to skewness and outliers than the mean. Modeling the quantiles instead of the mean not only improves the robustness of the model but also reveals a fuller picture of the data by fitting varying quantile functions. The proposed semi-parametric mixture of quantile regressions model is proven to be identifiable under certain weak conditions. A kernel density based EM-type algorithm is developed to estimate the model parameters, while a stochastic version of the EM-type algorithm is constructed for the variance estimation. A couple of simulation studies and several real data applications are conducted to show the effectiveness of the proposed model.

Suggested Citation

  • Wu, Qiang & Yao, Weixin, 2016. "Mixtures of quantile regressions," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 162-176.
    • Handle: RePEc:eee:csdana:v:93:y:2016:i:c:p:162-176
    DOI: 10.1016/j.csda.2014.04.014
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    References listed on IDEAS

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    1. Song, Weixing & Yao, Weixin & Xing, Yanru, 2014. "Robust mixture regression model fitting by Laplace distribution," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 128-137.
    2. David Hunter & Derek Young, 2012. "Semiparametric mixtures of regressions," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(1), pages 19-38.
    3. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    4. Ingrassia, Salvatore & Minotti, Simona C. & Punzo, Antonio, 2014. "Model-based clustering via linear cluster-weighted models," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 159-182.
    5. Wayne DeSarbo & William Cron, 1988. "A maximum likelihood methodology for clusterwise linear regression," Journal of Classification, Springer;The Classification Society, vol. 5(2), pages 249-282, September.
    6. Wu, Qiang & Sampson, Allan R., 2009. "Mixture modeling with applications in schizophrenia research," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2563-2572, May.
    7. Yao, Weixin & Wei, Yan & Yu, Chun, 2014. "Robust mixture regression using the t-distribution," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 116-127.
    8. Gerhard Arminger & Petra Stein & Jörg Wittenberg, 1999. "Mixtures of conditional mean- and covariance-structure models," Psychometrika, Springer;The Psychometric Society, vol. 64(4), pages 475-494, December.
    9. García-Escudero, L.A. & Gordaliza, A. & Mayo-Iscar, A. & San Martín, R., 2010. "Robust clusterwise linear regression through trimming," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3057-3069, December.
    10. Bai, Xiuqin & Yao, Weixin & Boyer, John E., 2012. "Robust fitting of mixture regression models," Computational Statistics & Data Analysis, Elsevier, vol. 56(7), pages 2347-2359.
    11. Salvatore Ingrassia & Simona Minotti & Giorgio Vittadini, 2012. "Local Statistical Modeling via a Cluster-Weighted Approach with Elliptical Distributions," Journal of Classification, Springer;The Classification Society, vol. 29(3), pages 363-401, October.
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    Cited by:

    1. Hu, Hao & Yao, Weixin & Wu, Yichao, 2017. "The robust EM-type algorithms for log-concave mixtures of regression models," Computational Statistics & Data Analysis, Elsevier, vol. 111(C), pages 14-26.
    2. Maruotti, Antonello & Petrella, Lea & Sposito, Luca, 2021. "Hidden semi-Markov-switching quantile regression for time series," Computational Statistics & Data Analysis, Elsevier, vol. 159(C).
    3. Ang Shan & Fengkai Yang, 2021. "Bayesian Inference for Finite Mixture Regression Model Based on Non-Iterative Algorithm," Mathematics, MDPI, vol. 9(6), pages 1-13, March.
    4. Hong Li & Qifan Song & Jianxi Su, 2021. "Robust estimates of insurance misrepresentation through kernel quantile regression mixtures," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 88(3), pages 625-663, September.

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