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Small area estimation under a spatially non-linear model

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  • Chandra, Hukum
  • Salvati, Nicola
  • Chambers, Ray

Abstract

We describe a methodology for small area estimation of counts that assumes an area-level version of a nonparametric generalized linear mixed model with a mean structure defined using spatial splines. The proposed method represents an alternative to other small area estimation methods based on area level spatial models that are designed for both spatially stationary and spatially non-stationary populations. We develop an estimator for the mean squared error of the proposed small area predictor as well as an approach for testing for the presence of spatial structure in the data and evaluate both the proposed small area predictor and its mean squared error estimator via simulations studies. Our empirical results show that when data are spatially non-stationary the proposed small area predictor outperforms other area level estimators in common use and that the proposed mean squared error estimator tracks the actual mean squared error reasonably well, with confidence intervals based on it achieving close to nominal coverage. An application to poverty estimation using household consumer expenditure survey data from 2011–12 collected by the national sample survey office of India is presented.

Suggested Citation

  • Chandra, Hukum & Salvati, Nicola & Chambers, Ray, 2018. "Small area estimation under a spatially non-linear model," Computational Statistics & Data Analysis, Elsevier, vol. 126(C), pages 19-38.
    • Handle: RePEc:eee:csdana:v:126:y:2018:i:c:p:19-38
    DOI: 10.1016/j.csda.2018.04.002
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    References listed on IDEAS

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    1. Gonzalez-Manteiga, W. & Lombardia, M.J. & Molina, I. & Morales, D. & Santamaria, L., 2007. "Estimation of the mean squared error of predictors of small area linear parameters under a logistic mixed model," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2720-2733, February.
    2. Nikos Tzavidis & Nicola Salvati & Monica Pratesi & Ray Chambers, 2008. "M-quantile models with application to poverty mapping," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 17(3), pages 393-411, July.
    3. Isabel Molina & Ayoub Saei & M. José Lombardía, 2007. "Small area estimates of labour force participation under a multinomial logit mixed model," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 170(4), pages 975-1000, October.
    4. Pang Du & Yihua Jiang & Yuedong Wang, 2011. "Smoothing Spline ANOVA Frailty Model for Recurrent Event Data," Biometrics, The International Biometric Society, vol. 67(4), pages 1330-1339, December.
    5. 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.
    6. Miguel Boubeta & María José Lombardía & Domingo Morales, 2016. "Empirical best prediction under area-level Poisson mixed models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(3), pages 548-569, September.
    7. Hukum Chandra & Nicola Salvati & U. C. Sud, 2011. "Disaggregate-level estimates of indebtedness in the state of Uttar Pradesh in India: an application of small-area estimation technique," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(11), pages 2413-2432, January.
    8. Boubeta, Miguel & Lombardía, María José & Morales, Domingo, 2017. "Poisson mixed models for studying the poverty in small areas," Computational Statistics & Data Analysis, Elsevier, vol. 107(C), pages 32-47.
    9. Hukum Chandra & Nicola Salvati, 2018. "Small area estimation of proportions under a spatial dependent aggregated level random effects model," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(5), pages 1234-1255, March.
    10. J. D. Opsomer & G. Claeskens & M. G. Ranalli & G. Kauermann & F. J. Breidt, 2008. "Non‐parametric small area estimation using penalized spline regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 265-286, February.
    11. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, September.
    12. Esther López-Vizcaíno & María José Lombardía & Domingo Morales, 2015. "Small area estimation of labour force indicators under a multinomial model with correlated time and area effects," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 178(3), pages 535-565, June.
    13. M. Ugarte & A. Militino & T. Goicoa, 2009. "Benchmarked estimates in small areas using linear mixed models with restrictions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(2), pages 342-364, August.
    14. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, September.
    15. M. P. Wand, 2003. "Smoothing and mixed models," Computational Statistics, Springer, vol. 18(2), pages 223-249, July.
    16. Inyoung Kim & Noah D. Cohen & Raymond J. Carroll, 2003. "Semiparametric Regression Splines in Matched Case-Control Studies," Biometrics, The International Biometric Society, vol. 59(4), pages 1158-1169, December.
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    2. Priyanka Anjoy, 2023. "Hierarchical Bayes Measurement Error Small Area Model for Estimation of Disaggregated Level Workers Mobility Pattern in India," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 21(2), pages 339-361, June.
    3. Ashutosh & Piyush Kant Rai & Ajeet Kumar Singh, 2023. "A Comparative Study on Calibration Approach Based Estimators for Domain Estimation Utilizing Power Function: Revisited," Annals of Data Science, Springer, vol. 10(6), pages 1559-1569, December.

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