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Bias Adjusted Estimation for Small Areas with Outlying Values

Bias Adjusted Estimation for Small Areas with Outlying Values
Bias Adjusted Estimation for Small Areas with Outlying Values
Small area estimation techniques typically rely on regression models that use both covariates and random effects to explain between domain variation. Chambers and Tzavidis (2006) describe a novel approach to small area estimation that is based on modelling quantile-like parameters of the conditional distribution of the target variable given the covariates. This is an outlier robust approach that avoids conventional Gaussian assumptions and the problems associated with specification of random effects, allowing inter-domain differences to be characterized by the variation of area-specific M-quantile coefficients. These authors observed, however, that M-quantile estimates of small area means are biased with the magnitude of the bias being related to the presence of outliers in the data. In this paper we propose a bias adjustment to the M-quantile small area estimator of the mean that is based on representing this estimator as a functional of the small area distribution function. The method is then generalized for estimating other quantiles of the distribution function in a small area. The effect of this bias adjustment on small area estimation with random effects models in the presence of model misspecification is also examined.
M06/09
Southampton Statistical Sciences Research Institute, University of Southampton
Tzavidis, Nikos
431ec55d-c147-466d-9c65-0f377b0c1f6a
Chambers, Ray
96331700-f45e-4483-a887-fef921888ff2
Tzavidis, Nikos
431ec55d-c147-466d-9c65-0f377b0c1f6a
Chambers, Ray
96331700-f45e-4483-a887-fef921888ff2

Tzavidis, Nikos and Chambers, Ray (2006) Bias Adjusted Estimation for Small Areas with Outlying Values (S3RI Methodology Working Papers, M06/09) Southampton, UK. Southampton Statistical Sciences Research Institute, University of Southampton 26pp.

Record type: Monograph (Working Paper)

Abstract

Small area estimation techniques typically rely on regression models that use both covariates and random effects to explain between domain variation. Chambers and Tzavidis (2006) describe a novel approach to small area estimation that is based on modelling quantile-like parameters of the conditional distribution of the target variable given the covariates. This is an outlier robust approach that avoids conventional Gaussian assumptions and the problems associated with specification of random effects, allowing inter-domain differences to be characterized by the variation of area-specific M-quantile coefficients. These authors observed, however, that M-quantile estimates of small area means are biased with the magnitude of the bias being related to the presence of outliers in the data. In this paper we propose a bias adjustment to the M-quantile small area estimator of the mean that is based on representing this estimator as a functional of the small area distribution function. The method is then generalized for estimating other quantiles of the distribution function in a small area. The effect of this bias adjustment on small area estimation with random effects models in the presence of model misspecification is also examined.

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Published date: 14 June 2006

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Local EPrints ID: 38976
URI: http://eprints.soton.ac.uk/id/eprint/38976
PURE UUID: f8ed13d9-6df3-4140-a6fe-3a7981c90fd3
ORCID for Nikos Tzavidis: ORCID iD orcid.org/0000-0002-8413-8095

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Date deposited: 14 Jun 2006
Last modified: 16 Mar 2024 03:23

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Contributors

Author: Nikos Tzavidis ORCID iD
Author: Ray Chambers

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