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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 Neutralizing Capacity for lakes in the north-east of the USA.
borrowing strength over space, environmental data, estimation for out of sample areas, robust regression, spatial dependency
M10/12
Southampton Statistical Sciences Research Institute, University of Southampton
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 (S3RI Methodology Working Papers, M10/12) Southampton, GB. Southampton Statistical Sciences Research Institute, University of Southampton 26pp. (Submitted)

Record type: Monograph (Working Paper)

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 Neutralizing Capacity for lakes in the north-east of the USA.

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More information

Submitted date: 5 October 2010
Keywords: borrowing strength over space, environmental data, estimation for out of sample areas, robust regression, spatial dependency

Identifiers

Local EPrints ID: 164935
URI: http://eprints.soton.ac.uk/id/eprint/164935
PURE UUID: 93fa8c6b-66a9-48b1-b72c-f40228e9d6f7
ORCID for N. Tzavidis: ORCID iD orcid.org/0000-0002-8413-8095

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Date deposited: 07 Oct 2010 09:01
Last modified: 14 Mar 2024 02:46

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Contributors

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

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