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Small area estimation via M-quantile geographically weighted regression

Small area estimation via M-quantile geographically weighted regression
Small area estimation via M-quantile geographically weighted regression
The effective use of spatial information, that is, the geographic locations of population units, in a regression model-based approach to small area estimation is an important practical issue. One approach for incorporating such spatial information in a small area regression model is via Geographically Weighted Regression (GWR). In GWR, the relationship between the outcome variable and the covariates is characterised by local rather than global parameters, where local is defined spatially. In this paper, we investigate GWR-based small area estimation under the M-quantile modelling approach. In particular, we specify an M-quantile GWR model that is a local model for the M-quantiles of the conditional distribution of the outcome variable given the covariates. This model is then used to define a bias-robust predictor of the small area characteristic of interest that also accounts for spatial association in the data. An important spin-off from applying the M-quantile GWR small area model is that it can potentially offer more efficient synthetic estimation for out of sample areas. We demonstrate the usefulness of this framework through both model-based as well as design-based simulations, with the latter based on a realistic survey data set. The paper concludes with an illustrative application that focuses on estimation of average levels of Acid Neutralising Capacity for lakes in the Northeast of the USA.
borrowing strength over space, environmental data, estimation for out of sample areas, robust regression, spatial dependency
1133-0686
Salvati, N.
d1b7ebe3-afad-40fb-b32c-e748e344e922
Tzavidis, N.
431ec55d-c147-466d-9c65-0f377b0c1f6a
Pratesi, M.
083eb444-b19b-4e6b-bb39-cc182bea9412
Chambers, R.
a9a457b3-2dc5-4ff0-9ed3-dbb3a6901ed7
Salvati, N.
d1b7ebe3-afad-40fb-b32c-e748e344e922
Tzavidis, N.
431ec55d-c147-466d-9c65-0f377b0c1f6a
Pratesi, M.
083eb444-b19b-4e6b-bb39-cc182bea9412
Chambers, R.
a9a457b3-2dc5-4ff0-9ed3-dbb3a6901ed7

Salvati, N., Tzavidis, N., Pratesi, M. and Chambers, R. (2010) Small area estimation via M-quantile geographically weighted regression. Test. (doi:10.1007/s11749-010-0231-1).

Record type: Article

Abstract

The effective use of spatial information, that is, the geographic locations of population units, in a regression model-based approach to small area estimation is an important practical issue. One approach for incorporating such spatial information in a small area regression model is via Geographically Weighted Regression (GWR). In GWR, the relationship between the outcome variable and the covariates is characterised by local rather than global parameters, where local is defined spatially. In this paper, we investigate GWR-based small area estimation under the M-quantile modelling approach. In particular, we specify an M-quantile GWR model that is a local model for the M-quantiles of the conditional distribution of the outcome variable given the covariates. This model is then used to define a bias-robust predictor of the small area characteristic of interest that also accounts for spatial association in the data. An important spin-off from applying the M-quantile GWR small area model is that it can potentially offer more efficient synthetic estimation for out of sample areas. We demonstrate the usefulness of this framework through both model-based as well as design-based simulations, with the latter based on a realistic survey data set. The paper concludes with an illustrative application that focuses on estimation of average levels of Acid Neutralising Capacity for lakes in the Northeast of the USA.

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More information

Published date: 24 December 2010
Keywords: borrowing strength over space, environmental data, estimation for out of sample areas, robust regression, spatial dependency

Identifiers

Local EPrints ID: 181885
URI: http://eprints.soton.ac.uk/id/eprint/181885
ISSN: 1133-0686
PURE UUID: 0568a72f-fda2-464f-94fa-a9cde6f78e2f
ORCID for N. Tzavidis: ORCID iD orcid.org/0000-0002-8413-8095

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Date deposited: 26 Apr 2011 09:31
Last modified: 15 Mar 2024 03:11

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Contributors

Author: N. Salvati
Author: N. Tzavidis ORCID iD
Author: M. Pratesi
Author: R. Chambers

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