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An outlier robust block bootstrap for small area estimation

Conference Paper


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Abstract


  • Small area inference based on mixed models, i.e. models that contain both fixed and

    random effects, are the industry standard for this field, allowing between area

    heterogeneity to be represented by random area effects. Use of the linear mixed model

    is ubiquitous in this context, with maximum likelihood, or its close relative, REML,

    the standard method for estimating the parameters of this model. These parameter

    estimates, and in particular the resulting predicted values of the random area effects,

    are then used to construct empirical best linear unbiased predictors (EBLUPs) of the

    unknown small area means. It is now well known that the EBLUP can be unstable

    when there are outliers in sample data, and an outlier-robust EBLUP, or REBLUP, has

    been proposed by Sinha and Rao (2009), based on modifying the parameter estimating

    functions to make them less sensitive to sample outliers. Unfortunately, these

    modified estimating functions can be numerically unstable, and mean squared error

    estimation for the REBLUP is not straightforward. Taking a somewhat different

    approach, Chambers and Mokhtarian (2013) proposed an outlier robust block

    bootstrap approach to fitting a linear mixed model in the presence of both area level

    and unit level outliers. A natural extension of this bounded block bootstrap can then be

    used to define an outlier robust version of the EBLUP and a simple way of estimating

    its mean squared error. This approach is described in this paper, together with

    simulation results that provides some evidence for our claim that the new method is

    robust to the influence of outliers. In particular, it leads to an easily computed version

    of the REBLUP and an easily computed and stable estimate of its mean squared error.

Publication Date


  • 2013

Citation


  • Mokhtarian, P. & Chambers, R. (2013). An outlier robust block bootstrap for small area estimation. Proceedings of the 59th World Statistics Congress of the International Statistical Institute (pp. 798-803). Hague, Netherlands: International Statistical Institute.

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=2942&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/1933

Start Page


  • 798

End Page


  • 803

Place Of Publication


  • http://2013.isiproceedings.org/index.php?r1=AS&r5=All&Browse=Go

Abstract


  • Small area inference based on mixed models, i.e. models that contain both fixed and

    random effects, are the industry standard for this field, allowing between area

    heterogeneity to be represented by random area effects. Use of the linear mixed model

    is ubiquitous in this context, with maximum likelihood, or its close relative, REML,

    the standard method for estimating the parameters of this model. These parameter

    estimates, and in particular the resulting predicted values of the random area effects,

    are then used to construct empirical best linear unbiased predictors (EBLUPs) of the

    unknown small area means. It is now well known that the EBLUP can be unstable

    when there are outliers in sample data, and an outlier-robust EBLUP, or REBLUP, has

    been proposed by Sinha and Rao (2009), based on modifying the parameter estimating

    functions to make them less sensitive to sample outliers. Unfortunately, these

    modified estimating functions can be numerically unstable, and mean squared error

    estimation for the REBLUP is not straightforward. Taking a somewhat different

    approach, Chambers and Mokhtarian (2013) proposed an outlier robust block

    bootstrap approach to fitting a linear mixed model in the presence of both area level

    and unit level outliers. A natural extension of this bounded block bootstrap can then be

    used to define an outlier robust version of the EBLUP and a simple way of estimating

    its mean squared error. This approach is described in this paper, together with

    simulation results that provides some evidence for our claim that the new method is

    robust to the influence of outliers. In particular, it leads to an easily computed version

    of the REBLUP and an easily computed and stable estimate of its mean squared error.

Publication Date


  • 2013

Citation


  • Mokhtarian, P. & Chambers, R. (2013). An outlier robust block bootstrap for small area estimation. Proceedings of the 59th World Statistics Congress of the International Statistical Institute (pp. 798-803). Hague, Netherlands: International Statistical Institute.

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=2942&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/1933

Start Page


  • 798

End Page


  • 803

Place Of Publication


  • http://2013.isiproceedings.org/index.php?r1=AS&r5=All&Browse=Go