The University of Southampton
University of Southampton Institutional Repository

Estimation and testing in M-quantile regression with applications to small area estimation

Estimation and testing in M-quantile regression with applications to small area estimation
Estimation and testing in M-quantile regression with applications to small area estimation
In recent years, M-quantile regression has been applied to small area estimation to obtain reliable and outlier robust estimators without recourse to strong parametric assumptions. In this paper, after a review of M-quantile regression and its application to small area estimation, we cover several topics related to model specification and selection for M-quantile regression that received little attention so far. Specifically, a pseudo-R2 goodness-of-fit measure is proposed, along with likelihood ratio and Wald type tests for model specification. A test to assess the presence of actual area heterogeneity in the data is also proposed. Finally, we introduce a new estimator of the scale of the regression residuals, motivated by a representation of the M-quantile regression estimation as a regression model with Generalised Asymmetric Least Informative distributed error terms. The Generalised Asymmetric Least Informative distribution, introduced in this paper, generalises the asymmetric Laplace distribution often associated to quantile regression. As the testing procedures discussed in the paper are motivated asymptotically, their finite sample properties are empirically assessed in Monte Carlo simulations. Although the proposed methods apply generally to Mquantile regression, in this paper, their use ar illustrated by means of an application to Small Area Estimation using a well known real dataset.
0306-7734
Bianchi, Annamaria
93cab0e9-6745-4c30-8488-eed0f518b88c
Fabrizi, Enrico
b8cbe145-06b2-4756-b169-393a4905521d
Salvati, Nicola
9be298e5-de55-4a24-9361-054a2ec09726
Tzavidis, Nikolaos
431ec55d-c147-466d-9c65-0f377b0c1f6a
Bianchi, Annamaria
93cab0e9-6745-4c30-8488-eed0f518b88c
Fabrizi, Enrico
b8cbe145-06b2-4756-b169-393a4905521d
Salvati, Nicola
9be298e5-de55-4a24-9361-054a2ec09726
Tzavidis, Nikolaos
431ec55d-c147-466d-9c65-0f377b0c1f6a

Bianchi, Annamaria, Fabrizi, Enrico, Salvati, Nicola and Tzavidis, Nikolaos (2018) Estimation and testing in M-quantile regression with applications to small area estimation. International Statistical Review. (doi:10.1111/insr.12267).

Record type: Article

Abstract

In recent years, M-quantile regression has been applied to small area estimation to obtain reliable and outlier robust estimators without recourse to strong parametric assumptions. In this paper, after a review of M-quantile regression and its application to small area estimation, we cover several topics related to model specification and selection for M-quantile regression that received little attention so far. Specifically, a pseudo-R2 goodness-of-fit measure is proposed, along with likelihood ratio and Wald type tests for model specification. A test to assess the presence of actual area heterogeneity in the data is also proposed. Finally, we introduce a new estimator of the scale of the regression residuals, motivated by a representation of the M-quantile regression estimation as a regression model with Generalised Asymmetric Least Informative distributed error terms. The Generalised Asymmetric Least Informative distribution, introduced in this paper, generalises the asymmetric Laplace distribution often associated to quantile regression. As the testing procedures discussed in the paper are motivated asymptotically, their finite sample properties are empirically assessed in Monte Carlo simulations. Although the proposed methods apply generally to Mquantile regression, in this paper, their use ar illustrated by means of an application to Small Area Estimation using a well known real dataset.

Text
Bianchi_et_al-2017-International_Statistical_Review - Accepted Manuscript
Download (1MB)

More information

Accepted/In Press date: 10 March 2018
e-pub ahead of print date: 5 April 2018

Identifiers

Local EPrints ID: 419143
URI: https://eprints.soton.ac.uk/id/eprint/419143
ISSN: 0306-7734
PURE UUID: ba64ae06-9b08-455e-9010-277590ea2250

Catalogue record

Date deposited: 06 Apr 2018 16:30
Last modified: 14 Mar 2019 05:09

Export record

Altmetrics

Contributors

Author: Annamaria Bianchi
Author: Enrico Fabrizi
Author: Nicola Salvati

University divisions

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of https://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×