IDEAS home Printed from
   My bibliography  Save this article

Local stationarity in small area estimation models


  • Roberto Benedetti
  • Monica Pratesi
  • Nicola Salvati


Small area estimators are often based on linear mixed models under the assumption that relationships among variables are stationary across the area of interest (Fay–Herriot models). This hypothesis is patently violated when the population is divided into heterogeneous latent subgroups. In this paper we propose a local Fay–Herriot model assisted by a Simulated Annealing algorithm to identify the latent subgroups of small areas. The value minimized through the Simulated Annealing algorithm is the sum of the estimated mean squared error (MSE) of the small area estimates. The technique is employed for small area estimates of erosion on agricultural land within the Rathbun Lake Watershed (IA, USA). The results are promising and show that introducing local stationarity in a small area model may lead to useful improvements in the performance of the estimators. Copyright Springer-Verlag 2013

Suggested Citation

  • Roberto Benedetti & Monica Pratesi & Nicola Salvati, 2013. "Local stationarity in small area estimation models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 22(1), pages 81-95, March.
  • Handle: RePEc:spr:stmapp:v:22:y:2013:i:1:p:81-95
    DOI: 10.1007/s10260-012-0208-1

    Download full text from publisher

    File URL:
    Download Restriction: Access to full text is restricted to subscribers.

    File URL:
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    1. Antonio Páez & Takashi Uchida & Kazuaki Miyamoto, 2002. "A General Framework for Estimation and Inference of Geographically Weighted Regression Models: 2. Spatial Association and Model Specification Tests," Environment and Planning A, , vol. 34(5), pages 883-904, May.
    2. Robert Tibshirani & Guenther Walther & Trevor Hastie, 2001. "Estimating the number of clusters in a data set via the gap statistic," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 411-423.
    3. Antonio Páez & Takashi Uchida & Kazuaki Miyamoto, 2002. "A General Framework for Estimation and Inference of Geographically Weighted Regression Models: 1. Location-Specific Kernel Bandwidths and a Test for Locational Heterogeneity," Environment and Planning A, , vol. 34(4), pages 733-754, April.
    4. Monica Pratesi & Nicola Salvati, 2008. "Small area estimation: the EBLUP estimator based on spatially correlated random area effects," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 17(1), pages 113-141, February.
    5. Maria Rita Sebastiani, 2003. "Markov random‐field models for estimating local labour markets," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 52(2), pages 201-211, May.
    6. Dimitris Fouskakis & David Draper, 2002. "Stochastic Optimization: a Review," International Statistical Review, International Statistical Institute, vol. 70(3), pages 315-349, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Duan Zhuang, 2006. "Spatial Dependence and Neighborhood Effects in Mortgage Lending: A Geographically Weighted Regression Approach," Working Paper 8571, USC Lusk Center for Real Estate.
    2. Wei, Chuan-Hua & Qi, Fei, 2012. "On the estimation and testing of mixed geographically weighted regression models," Economic Modelling, Elsevier, vol. 29(6), pages 2615-2620.
    3. Ingrid Nappi‐Choulet & Tristan‐Pierre Maury, 2011. "A Spatial And Temporal Autoregressive Local Estimation For The Paris Housing Market," Journal of Regional Science, Wiley Blackwell, vol. 51(4), pages 732-750, October.
    4. Paolo Postiglione & M. Andreano & Roberto Benedetti, 2013. "Using Constrained Optimization for the Identification of Convergence Clubs," Computational Economics, Springer;Society for Computational Economics, vol. 42(2), pages 151-174, August.
    5. Domenica Panzera & Paolo Postiglione, 2014. "Economic growth in Italian NUTS 3 provinces," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 53(1), pages 273-293, August.
    6. Alexis Comber & Khanh Chi & Man Q Huy & Quan Nguyen & Binbin Lu & Hoang H Phe & Paul Harris, 2020. "Distance metric choice can both reduce and induce collinearity in geographically weighted regression," Environment and Planning B, , vol. 47(3), pages 489-507, March.
    7. Thiemo Fetzer & Samuel Marden, 2017. "Take What You Can: Property Rights, Contestability and Conflict," Economic Journal, Royal Economic Society, vol. 0(601), pages 757-783, May.
    8. Daniel Agness & Travis Baseler & Sylvain Chassang & Pascaline Dupas & Erik Snowberg, 2022. "Valuing the Time of the Self-Employed," CESifo Working Paper Series 9567, CESifo.
    9. Batool, Fatima & Hennig, Christian, 2021. "Clustering with the Average Silhouette Width," Computational Statistics & Data Analysis, Elsevier, vol. 158(C).
    10. Nicoleta Serban & Huijing Jiang, 2012. "Multilevel Functional Clustering Analysis," Biometrics, The International Biometric Society, vol. 68(3), pages 805-814, September.
    11. Orietta Nicolis & Jean Paul Maidana & Fabian Contreras & Danilo Leal, 2024. "Analyzing the Impact of COVID-19 on Economic Sustainability: A Clustering Approach," Sustainability, MDPI, vol. 16(4), pages 1-30, February.
    12. Li, Pai-Ling & Chiou, Jeng-Min, 2011. "Identifying cluster number for subspace projected functional data clustering," Computational Statistics & Data Analysis, Elsevier, vol. 55(6), pages 2090-2103, June.
    13. Yaeji Lim & Hee-Seok Oh & Ying Kuen Cheung, 2019. "Multiscale Clustering for Functional Data," Journal of Classification, Springer;The Classification Society, vol. 36(2), pages 368-391, July.
    14. Forzani, Liliana & Gieco, Antonella & Tolmasky, Carlos, 2017. "Likelihood ratio test for partial sphericity in high and ultra-high dimensions," Journal of Multivariate Analysis, Elsevier, vol. 159(C), pages 18-38.
    15. Yujia Li & Xiangrui Zeng & Chien‐Wei Lin & George C. Tseng, 2022. "Simultaneous estimation of cluster number and feature sparsity in high‐dimensional cluster analysis," Biometrics, The International Biometric Society, vol. 78(2), pages 574-585, June.
    16. Vojtech Blazek & Michal Petruzela & Tomas Vantuch & Zdenek Slanina & Stanislav Mišák & Wojciech Walendziuk, 2020. "The Estimation of the Influence of Household Appliances on the Power Quality in a Microgrid System," Energies, MDPI, vol. 13(17), pages 1-21, August.
    17. Jan Pablo Burgard & Domingo Morales & Anna-Lena Wölwer, 2022. "Small area estimation of socioeconomic indicators for sampled and unsampled domains," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(2), pages 287-314, June.
    18. Yogi Vidyattama & Robert Tanton & Nicholas Biddle, 2015. "Estimating small-area Indigenous cultural participation from synthetic survey data," Environment and Planning A, , vol. 47(5), pages 1211-1228, May.
    19. Dian Handayani & Henk Folmer & Anang Kurnia & Khairil Anwar Notodiputro, 2018. "The spatial empirical Bayes predictor of the small area mean for a lognormal variable of interest and spatially correlated random effects," Empirical Economics, Springer, vol. 55(1), pages 147-167, August.
    20. Andrew Clark & Alexander Mihailov & Michael Zargham, 2021. "Complex Systems Modeling of Community Inclusion Currencies," Economics Discussion Papers em-dp2021-06, Department of Economics, University of Reading.


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:stmapp:v:22:y:2013:i:1:p:81-95. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.