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A Two-Part Geoadditive Small Area Model for Geographical Domain Estimation

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Topics in Theoretical and Applied Statistics

Part of the book series: Studies in Theoretical and Applied Statistics ((STASSPSS))

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Abstract

We are interested in estimating small domain means of a response variable that shows a spatial trend and has a continuous skewed distribution with a large number of values clustered at zero. This kind of variable can occur in many surveys, like business or agricultural surveys: examples are the quantity of crops produced or the amount of land allocated for their production collected by the Farm Structure Survey driven by the Italian Statistical Institute. The small sample size within the areas requires the use of small area model dependent methods to increase the effective area sample size by using census and administrative auxiliary data. To account simultaneously for the excess of zeros, the skewness of the distribution and the possible spatial trend of the data, we present a two-part geoadditive small area model. An application to the estimation of the per-farm average grapevine production in Tuscany at Agrarian Region level shows the satisfactory performance of the model.

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Notes

  1. 1.

    Statistics are produced using expert information. Data are provided by local authorities that collect experts evaluations on area and yield of different crops (Source: http://siqual.istat.it).

References

  1. Battese, G.E., Harter, R.M., Fuller, W.A.: An error component model for prediction of county crop areas using survey and satellite data. J. Am. Stat. Assoc. 83, 28–36 (1988)

    Article  Google Scholar 

  2. Bocci, C., Petrucci, A., Rocco, E.: Geographically weighted regression for small area estimation: an agricultural case study. In: Proceedings of the XLIII Scientific Meeting of the Italian Statistical Society, CLEUP, pp. 615–618 (2006)

    Google Scholar 

  3. Chandra, H., Chambers, R.: Small area estimation under transformation to linearity. Surv. Methodol. 37, 39–51 (2011)

    Google Scholar 

  4. Chandra, H., Chambers, R.: Small area estimation for skewed data in presence of zeros. Calcutta Stat. Assoc. Bull. 63, 249–252 (2011)

    MathSciNet  Google Scholar 

  5. Chandra, H., Sud, U.: Small area estimation for zero-inflated data. Commun. Stat. Simul. Comput. 41, 632–643 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  6. Cressie, N.: Statistics for Spatial Data (revised edition). Wiley, New York (1993)

    MATH  Google Scholar 

  7. Fay, R.E., Herriot, R.A.: Estimation of income from small places: an application of James-Stein procedures to census data. J. Am. Stat. Assoc. 74, 269–277 (1979)

    Article  MathSciNet  Google Scholar 

  8. Gosh, P., Albert, P.S.: A Bayesian analysis for longitudinal semicontinuous data with an application to an acupuncture clinical trial. Comput. Stat. Data Anal. 53, 699–706 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  9. Hastie, T.J., Tibshirani, R.: Generalized Additive Models. Chapman & Hall, London (1990)

    MATH  Google Scholar 

  10. Kammann, E.E., Wand, M.P.: Geoadditive models. Appl. Stat. 52, 1–18 (2003)

    MathSciNet  MATH  Google Scholar 

  11. Kaufman, L., Rousseeuw, P.J.: Finding Groups in Data: An Introduction to Cluster Analysis. Wiley, New York (1990)

    Book  Google Scholar 

  12. Olsen, M.K., Schafer, J.L.: A two-part random-effects model for semicontinuous longitudinal data. J. Am. Stat. Assoc. 96, 730–745 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  13. Opsomer, J.D., Claeskens, G., Ranalli, M.G., Kauermann, G., Breidt, F.J.: Non-parametric small area estimation using penalized spline regression. J. R. Stat. Soc. Ser. B 70, 265–286 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  14. Pfeffermann, D., Terryn, B., Moura, F.A.S.: Small area estimation under a two-part random effects model with application to estimation of literacy in developing countries. Surv. Methodol. 34, 235–249 (2008)

    Google Scholar 

  15. Ruppert, D., Wand, M.P., Carroll, R.J.: Semiparametric Regression. Cambridge University Press, Cambridge (2003)

    Book  MATH  Google Scholar 

  16. Slud, E.V., Maiti, T.: Small-area estimation based on survey data from a left-censored Fay-Herriot model. J. Stat. Plann. Inference 141, 3520–3535 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  17. Zhang, M., Strawederman, R.L., Cowen, M., Wells, M.E.: Bayesian inference for a two-part hierarchical model: an application to profiling providers in managed health care. J. Am. Stat. Assoc. 101, 934–945 (2006)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. IRPET - Regional Institute for Economic Planning of Tuscany, Via Pietro Dazzi 1, 50141, Firenze, Italy

    Chiara Bocci

  2. Department of Statistics, Computer Science, Applications “G. Parenti”, University of Florence, Viale Morgagni 59, 50134, Firenze, Italy

    Alessandra Petrucci & Emilia Rocco

Authors
  1. Chiara Bocci
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  2. Alessandra Petrucci
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  3. Emilia Rocco
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Corresponding author

Correspondence to Emilia Rocco .

Editor information

Editors and Affiliations

  1. MEMOTEF, Sapienza University of Rome, Rome, Italy

    Giorgio Alleva

  2. Dept. of Statistcs & Informatics, University of Florence, Florence, Italy

    Andrea Giommi

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Bocci, C., Petrucci, A., Rocco, E. (2016). A Two-Part Geoadditive Small Area Model for Geographical Domain Estimation. In: Alleva, G., Giommi, A. (eds) Topics in Theoretical and Applied Statistics. Studies in Theoretical and Applied Statistics(). Springer, Cham. https://doi.org/10.1007/978-3-319-27274-0_12

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