Marginal M-quantile regression for multivariate dependent data
Marginal M-quantile regression for multivariate dependent data
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.
Asymptotic properties, Correlated data, Directional M-quantile, Generalized M-quantile estimating equations, M-quantile contour
Merlo, Luca
436fb4df-938c-4b5d-aedc-d68e85390a36
Petrella, Lea
bf351458-2a5a-452e-be73-496a19c4060a
Salvati, Nicola
9be298e5-de55-4a24-9361-054a2ec09726
Tzavidis, Nikolaos
431ec55d-c147-466d-9c65-0f377b0c1f6a
19 April 2022
Merlo, Luca
436fb4df-938c-4b5d-aedc-d68e85390a36
Petrella, Lea
bf351458-2a5a-452e-be73-496a19c4060a
Salvati, Nicola
9be298e5-de55-4a24-9361-054a2ec09726
Tzavidis, Nikolaos
431ec55d-c147-466d-9c65-0f377b0c1f6a
Merlo, Luca, Petrella, Lea, Salvati, Nicola and Tzavidis, Nikolaos
(2022)
Marginal M-quantile regression for multivariate dependent data.
Computational Statistics & Data Analysis, 173, [107500].
(doi:10.1016/j.csda.2022.107500).
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.
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Accepted/In Press date: 5 April 2022
e-pub ahead of print date: 7 April 2022
Published date: 19 April 2022
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© 2022 Elsevier B.V.
Keywords:
Asymptotic properties, Correlated data, Directional M-quantile, Generalized M-quantile estimating equations, M-quantile contour
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Local EPrints ID: 457607
URI: http://eprints.soton.ac.uk/id/eprint/457607
ISSN: 0167-9473
PURE UUID: 3ba3be88-ba30-42ef-9c33-f46687a19289
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Date deposited: 14 Jun 2022 16:37
Last modified: 17 Mar 2024 02:54
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Contributors
Author:
Luca Merlo
Author:
Lea Petrella
Author:
Nicola Salvati
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