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Marginal M-quantile regression for multivariate dependent data

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  • Merlo, Luca
  • Petrella, Lea
  • Salvati, Nicola
  • Tzavidis, Nikos

Abstract

An M-quantile regression model is developed for the analysis of multiple dependent outcomes by introducing the notion of directional M-quantiles for multivariate responses. In order to incorporate the correlation structure of the data into the estimation framework, a robust marginal M-quantile model is proposed extending the well-known generalized estimating equations approach to the case of regression M-quantiles with Huber's loss function. The estimation of the model and the asymptotic properties of estimators are discussed. In addition, the idea of M-quantile contours is introduced to describe the dependence between the response variables and to investigate the effect of covariates on the location, spread and shape of the distribution of the responses. To examine their variability, confidence envelopes via nonparametric bootstrap are constructed. The validity of the proposed methodology is explored both by means of simulation studies and through an application to educational data.

Suggested Citation

  • Merlo, Luca & Petrella, Lea & Salvati, Nicola & Tzavidis, Nikos, 2022. "Marginal M-quantile regression for multivariate dependent data," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
    • Handle: RePEc:eee:csdana:v:173:y:2022:i:c:s0167947322000809
    DOI: 10.1016/j.csda.2022.107500
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    Cited by:

    1. Ochoa Arellano, Maicol Jesús & Cascos Fernández, Ignacio, 2022. "Data depth and multiple output regression, the distorted M-quantiles approach," DES - Working Papers. Statistics and Econometrics. WS 35465, Universidad Carlos III de Madrid. Departamento de Estadística.
    2. Valeria Bignozzi & Luca Merlo & Lea Petrella, 2022. "Inter-order relations between moments of a Student $t$ distribution, with an application to $L_p$-quantiles," Papers 2209.12855, arXiv.org.

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