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Model-based direct estimation of small-area distributions

Journal Article


Abstract


  • Much of the small-area estimation literature focuses on population totals and means. However, users of survey data are often interested in the finite-population distribution of a survey variable and in the measures (e.g. medians, quartiles, percentiles) that characterize the shape of this distribution at the small-area level. In this paper we propose a model-based direct estimator (MBDE, Chandra and Chambers) of the small-area distribution function. The MBDE is defined as a weighted sum of sample data from the area of interest, with weights derived from the calibrated spline-based estimate of the finite-population distribution function introduced by Harms and Duchesne, under an appropriately specified regression model with random area effects. We also discuss the mean squared error estimation of the MBDE. Monte Carlo simulations based on both simulated and real data sets show that the proposed MBDE and its associated mean squared error estimator perform well when compared with alternative estimators of the area-specific finite-population distribution function.

Authors


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

Publication Date


  • 2012

Citation


  • Salvati, N., Chandra, H. & Chambers, R. L. (2012). Model-based direct estimation of small-area distributions. Australian and New Zealand Journal of Statistics, 54 (1), 103-123.

Scopus Eid


  • 2-s2.0-84868550689

Ro Metadata Url


  • http://ro.uow.edu.au/infopapers/2081

Number Of Pages


  • 20

Start Page


  • 103

End Page


  • 123

Volume


  • 54

Issue


  • 1

Abstract


  • Much of the small-area estimation literature focuses on population totals and means. However, users of survey data are often interested in the finite-population distribution of a survey variable and in the measures (e.g. medians, quartiles, percentiles) that characterize the shape of this distribution at the small-area level. In this paper we propose a model-based direct estimator (MBDE, Chandra and Chambers) of the small-area distribution function. The MBDE is defined as a weighted sum of sample data from the area of interest, with weights derived from the calibrated spline-based estimate of the finite-population distribution function introduced by Harms and Duchesne, under an appropriately specified regression model with random area effects. We also discuss the mean squared error estimation of the MBDE. Monte Carlo simulations based on both simulated and real data sets show that the proposed MBDE and its associated mean squared error estimator perform well when compared with alternative estimators of the area-specific finite-population distribution function.

Authors


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

Publication Date


  • 2012

Citation


  • Salvati, N., Chandra, H. & Chambers, R. L. (2012). Model-based direct estimation of small-area distributions. Australian and New Zealand Journal of Statistics, 54 (1), 103-123.

Scopus Eid


  • 2-s2.0-84868550689

Ro Metadata Url


  • http://ro.uow.edu.au/infopapers/2081

Number Of Pages


  • 20

Start Page


  • 103

End Page


  • 123

Volume


  • 54

Issue


  • 1