Unified unconditional regression for multivariate quantiles, M-quantiles and expectiles
Unified unconditional regression for multivariate quantiles, M-quantiles and expectiles
In this article, we develop a unified regression approach to model unconditional quantiles, M-quantiles and expectiles of multivariate dependent variables exploiting the multidimensional Huber’s function. To assess the impact of changes in the covariates across the entire unconditional distribution of the responses, we extend the work of Firpo, Fortin, and Lemieux by running a mean regression of the recentered influence function on the explanatory variables. We discuss the estimation procedure and establish the asymptotic properties of the derived estimators. A data-driven procedure is also presented to select the tuning constant of the Huber’s function. The validity of the proposed methodology is explored with simulation studies and through an application using the Survey of Household Income and Wealth 2016 conducted by the Bank of Italy. Supplementary materials for this article are available online.
Influence function, M-estimation, Multivariate data, RIF regression, Unconditional partial effect
Merlo, Luca
436fb4df-938c-4b5d-aedc-d68e85390a36
Petrella, Lea
bf351458-2a5a-452e-be73-496a19c4060a
Salvati, Nicola
9be298e5-de55-4a24-9361-054a2ec09726
Tzavidis, Nikos
431ec55d-c147-466d-9c65-0f377b0c1f6a
24 August 2023
Merlo, Luca
436fb4df-938c-4b5d-aedc-d68e85390a36
Petrella, Lea
bf351458-2a5a-452e-be73-496a19c4060a
Salvati, Nicola
9be298e5-de55-4a24-9361-054a2ec09726
Tzavidis, Nikos
431ec55d-c147-466d-9c65-0f377b0c1f6a
Merlo, Luca, Petrella, Lea, Salvati, Nicola and Tzavidis, Nikos
(2023)
Unified unconditional regression for multivariate quantiles, M-quantiles and expectiles.
Journal of the American Statistical Association.
(doi:10.1080/01621459.2023.2250512).
Abstract
In this article, we develop a unified regression approach to model unconditional quantiles, M-quantiles and expectiles of multivariate dependent variables exploiting the multidimensional Huber’s function. To assess the impact of changes in the covariates across the entire unconditional distribution of the responses, we extend the work of Firpo, Fortin, and Lemieux by running a mean regression of the recentered influence function on the explanatory variables. We discuss the estimation procedure and establish the asymptotic properties of the derived estimators. A data-driven procedure is also presented to select the tuning constant of the Huber’s function. The validity of the proposed methodology is explored with simulation studies and through an application using the Survey of Household Income and Wealth 2016 conducted by the Bank of Italy. Supplementary materials for this article are available online.
Text
Unified unconditional regression for multivariate quantiles M quantiles and expectiles
- Accepted Manuscript
More information
Accepted/In Press date: 14 August 2023
e-pub ahead of print date: 24 August 2023
Published date: 24 August 2023
Additional Information:
Publisher Copyright:
© 2023 American Statistical Association.
Keywords:
Influence function, M-estimation, Multivariate data, RIF regression, Unconditional partial effect
Identifiers
Local EPrints ID: 481544
URI: http://eprints.soton.ac.uk/id/eprint/481544
ISSN: 0162-1459
PURE UUID: c31c090f-860d-45c8-a7b6-c95235102bbe
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Date deposited: 01 Sep 2023 16:52
Last modified: 14 Aug 2024 04:01
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Contributors
Author:
Luca Merlo
Author:
Lea Petrella
Author:
Nicola Salvati
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