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Small area estimation using a nonparametric model-based direct estimator

Journal Article


Abstract


  • Nonparametric regression is widely used as a method of characterizing a non-linear

    relationship between a variable of interest and a set of covariates. Practical application of

    nonparametric regression methods in the field of small area estimation is fairly recent,

    and has so far focussed on the use of empirical best linear unbiased prediction under a

    model that combines a penalized spline (p-spline) fit and random area effects. The concept

    of model-based direct estimation is used to develop an alternative nonparametric approach

    to estimation of a small area mean. The suggested estimator is a weighted average of the

    sample values from the area, with weights derived from a linear regression model with

    random area effects extended to incorporate a smooth, nonparametrically specified trend.

    Estimation of the mean squared error of the proposed small area estimator is also discussed.

    Monte Carlo simulations based on both simulated and real datasets show that the

    proposed model-based direct estimator and its associated mean squared error estimator

    perform well. They are worth considering in small area estimation applications where

    the underlying population regression relationships are non-linear or have a complicated

    functional form.

Authors


  •   Salvati, Nicola (external author)
  •   Chandra, Hukum (external author)
  •   Ranalli, M. Giovanna (external author)
  •   Chambers, Raymond L.

Publication Date


  • 2010

Citation


  • Salvati, N., Chandra, H., Ranalli, M. & Chambers, R. L. (2010). Small area estimation using a nonparametric model-based direct estimator. Computational Statistics and Data Analysis, 54 (9), 2159-2171.

Scopus Eid


  • 2-s2.0-77955432641

Ro Metadata Url


  • http://ro.uow.edu.au/infopapers/1715

Number Of Pages


  • 12

Start Page


  • 2159

End Page


  • 2171

Volume


  • 54

Issue


  • 9

Abstract


  • Nonparametric regression is widely used as a method of characterizing a non-linear

    relationship between a variable of interest and a set of covariates. Practical application of

    nonparametric regression methods in the field of small area estimation is fairly recent,

    and has so far focussed on the use of empirical best linear unbiased prediction under a

    model that combines a penalized spline (p-spline) fit and random area effects. The concept

    of model-based direct estimation is used to develop an alternative nonparametric approach

    to estimation of a small area mean. The suggested estimator is a weighted average of the

    sample values from the area, with weights derived from a linear regression model with

    random area effects extended to incorporate a smooth, nonparametrically specified trend.

    Estimation of the mean squared error of the proposed small area estimator is also discussed.

    Monte Carlo simulations based on both simulated and real datasets show that the

    proposed model-based direct estimator and its associated mean squared error estimator

    perform well. They are worth considering in small area estimation applications where

    the underlying population regression relationships are non-linear or have a complicated

    functional form.

Authors


  •   Salvati, Nicola (external author)
  •   Chandra, Hukum (external author)
  •   Ranalli, M. Giovanna (external author)
  •   Chambers, Raymond L.

Publication Date


  • 2010

Citation


  • Salvati, N., Chandra, H., Ranalli, M. & Chambers, R. L. (2010). Small area estimation using a nonparametric model-based direct estimator. Computational Statistics and Data Analysis, 54 (9), 2159-2171.

Scopus Eid


  • 2-s2.0-77955432641

Ro Metadata Url


  • http://ro.uow.edu.au/infopapers/1715

Number Of Pages


  • 12

Start Page


  • 2159

End Page


  • 2171

Volume


  • 54

Issue


  • 9