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The Impact of Sampling Designs on Small Area Estimates for Business Data

Open Access
|Dec 2014

References

  1. Asparouhov, T. 2006. “General Multi-Level Modeling with Sampling Weights.” Communications in Statistics - Theory and Methods 35: 439-460. DOI: http://dx.doi.org/10.1080/03610920500476598.10.1080/03610920500476598
  2. Bates, D. 2011. Computational Methods for Mixed Models. Available at: http://cran.rproject.org/web/packages/lme4/vignettes/Theory.pdf (accessed October 16, 2014).
  3. Bates, D., M. Maechler, and B. Bolker. 2011. Linear Mixed-Effects Models Using S4
  4. Classes. R package Version: 0.999375-42. Available at: http://www.r-project.org/conferences/useR-2012/TutorialBates.pdf (accessed October 14, 2014).
  5. Battese, G.E., R.M. Harter, and W.A. Fuller. 1988. “An Error Component Model for Prediction of County Crop Areas Using Survey and Satellite Data.” Journal of the American Statistical Association 83: 28-36. DOI: http://dx.doi.org/10.1080/01621459.1988.10478561.10.1080/01621459.1988.10478561
  6. Berg, E. and H. Chandra. 2012. “Small Area Prediction for a Unit Level Lognormal Model.” Federal Committee on Statistical Methodology Research Conference. DOI: http://dx.doi.org/10.1016/j.csda.2014.03.007.10.1016/j.csda.2014.03.007
  7. Burgard, J.P., R. Mu¨nnich, and T. Zimmermann. 2012. “Small Area Modelling Under Complex Survey Designs for Business Data.” In Proceedings of the Fourth International Conference of Establishment Surveys, June 11-14, 2012. Montreal. Available at: http:// www.amstat.org/meetings/ices/2012/papers/301906.pdf (accessed Oct 16, 2014).
  8. Butar, F.B. and P. Lahiri. 2003. “On Measures of Uncertainty of Empirical Bayes Small- Area Estimators.” Journal of Statistical Planning and Inference 112: 63-76. DOI: http://dx.doi.org/10.1016/S0378-3758(02)00323-3.10.1016/S0378-3758(02)00323-3
  9. Chambers, R., and N. Tzavidis. 2006. “M-Quantile Models for Small Area Estimation.” Biometrika 93: 255-268. DOI: http://dx.doi.org/10.1093/biomet/93.2.255.10.1093/biomet/93.2.255
  10. Chatterjee, S., P. Lahiri, and H. Li. 2008. “Parametric Bootstrap Approximation to the Distribution of EBLUP and Related Prediction Intervals in Linear Mixed Models.” The Annals of Statistics 36: 1221-1245.10.1214/07-AOS512
  11. Choudhry, G.H., J.N.K. Rao, and M.A. Hidiroglou. 2012. “On Sample Allocation for Efficient Domain Estimation.” Survey Methodology 38: 23-29.
  12. Costa, A., A. Satorra, and E. Ventura. 2004. “Improving Both Domain and Total Area Estimation by Composition.” Statistics andOperations Research Transactions 28: 69-86.
  13. Datta, G.S. 2009. “Model-Based Approach to Small Area Estimation.” In Handbook of Statistics, Vol. 29B, 251-288. New York: Elsevier.10.1016/S0169-7161(09)00232-6
  14. Datta, G.S., and P. Lahiri. 2000. “A Unified Measure of Uncertainty of Estimated Best Linear Unbiased Predictors in Small Area Estimation Problems.” Statistica Sinica 10: 613-627.
  15. Eurostat. 2008. “NACE Rev. 2: Statistical Classification of Economic Activities in the European Community.” Eurostat methodologies and working papers, European Communities, cat. No. KS-RA-07-015-EN-N.
  16. Falorsi, P.D. and P. Righi. 2008. “A Balanced Sampling Approach for Multi-Way Stratification Designs for Small Area Estimation.” Survey Methodology 34: 223-234.
  17. Fay, R.E. and R.A. Herriot. 1979. “Estimation of Income for Small Places: An Application of James-Stein Procedures to Census Data.” Journal of the American Statistical Association 74: 269-277. DOI: http://dx.doi.org/10.1080/01621459.1979.10482505.10.1080/01621459.1979.10482505
  18. Gabler, S., M. Ganninger, and R. Münnich. 2012. “Optimal Allocation of the Sample Size to Strata Under Box Constraints.” Metrika 75: 15-161. DOI: http://dx.doi.org/10.1007/s00184-010-0319-3.10.1007/s00184-010-0319-3
  19. Gonzalez-Manteiga, W., M.J. Lombardı´a, I. Molina, D. Morales, and L. Santamarı´a. 2008. “Bootstrap Mean Squared Error of a Small-Area EBLUP.” Journal of Statistical Computation and Simulation 78: 443-462.10.1080/00949650601141811
  20. Harville, D.A. 2008. Matrix Algebra from a Statistician’s Perspective. New York: Springer.
  21. Hidiroglou, M.A. and P. Lavallee. 2009. “Sampling and Estimation in Business Surveys.” In Handbook of Statistics, Vol. 29A, 441-470. New York: Elsevier. Holmberg, A., P. Flisberg, and M. Ro¨nnqvist. 2002. “On the Choice of Sampling Design in Business Surveys with Several Important Study Variables.” R&D Report 2002:3, Statistics Sweden.10.1016/S0169-7161(08)00017-5
  22. Jiang, J. and P. Lahiri. 2006. “Mixed Model Prediction and Small Area Estimation.” Test 15: 1-96. DOI: http://dx.doi.org/10.1007/BF02595419.10.1007/BF02595419
  23. Kackar, R.N., and D.A. Harville. 1984. “Approximations for Standard Errors of Estimators of Fixed and Random Effect in Mixed Linear Models.” Journal of the American Statistical Association 79: 853-862. DOI: http://dx.doi.org/10.1080/01621459.1984.10477102.10.1080/01621459.1984.10477102
  24. Kolb, J.-P., R. Mu¨nnich, F. Volk, and T. Zimmermann. 2013. “TRItalia dataset.” In BLUE-ETS Deliverable D6.2: Best practice recommendations on variance estimation and small area estimation in business surveys, edited by R. Bernardini Papalia, C. Bruch, T. Enderle, S. Falorsi, A. Fasulo, E. Fernandez-Vazquez, M. Ferrante, J.P. Kolb, R. Mu¨nnich, S. Pacei, R. Priam, P. Righi, T. Schmid, N. Shlomo, F. Volk, and T. Zimmermann, 168-188. Available at: http://www.blue-ets.istat.it/fileadmin/deliverables/Deliverable6.2.pdf (accessed October 16, 2014).
  25. Lehtonen, R., C.-E. Särndal, and A. Veijanen. 2003. “The Effect of Model Choice in Estimation for Domains, Including Small Domains.” Survey Methodology 29: 33-44.
  26. Lehtonen, R., C.-E. Särndal, and A. Veijanen. 2005. “Does the Model Matter? Comparing Model-Assisted and Model-Dependent Estimators of Class Frequencies for Domains.” Statistics in Transition 7: 649-673.
  27. Lehtonen, R., C.-E. Särndal, A. Veijanen, and M. Myrskylä. 2006. “The Role of Models in Model-Assisted and Model-Dependent Estimation for Domains and Small Areas.” Workshop on survey sampling and methodology, Ventspils. Available at: http://home.lu.lv/~pm90015/workshop2006/papers/Workshop2006_04_Lehtonen.pdf (accessed October 16, 2014).
  28. Lehtonen, R. and A. Veijanen. 2009. “Design-Based Methods of Estimation for Domains and Small Areas.” In Handbook of Statistics, Vol. 29B, 219-249. New York: Elsevier.10.1016/S0169-7161(09)00231-4
  29. Lehtonen, R., A. Veijanen, M. Myrskylä, and M. Valaste. 2011. “Small Area Estimation of Indicators on Poverty and Social Exclusion.” Technical report, AMELI deliverable D2.2. Available at: http://www.uni-trier.de/fileadmin/fb4/projekte/SurveyStatisticsNet/Ameli_Deliverables/AMELI-WP2-D2.2.20110402.pdf (accessed October 16, 2014).
  30. Little, R.J. 2012. “Calibrated Bayes, an Alternative Inferential Paradigm for Official Statistics.” Journal of Official Statistics 28: 309-334.
  31. Longford, N.T. 2006. “Sample Size Calculation for Small Area Estimation.” Survey Methodology 32: 87-96.
  32. Molina, I., and J.N.K. Rao. 2010. “Small Area Estimation of Poverty Indicators.” Canadian Journal of Statistics 38: 369-385. DOI: http://dx.doi.org/10.1002/cjs.10051.10.1002/cjs.10051
  33. Münnich, R. and J.P. Burgard. 2012. “On the Influence of Sampling Design on Small Area Estimates.” Journal of the Indian Society of Agricultural Statistics 66: 145-156.
  34. Münnich, R., E. Sachs, and M. Wagner. 2012. “Numerical Solution of Optimal Allocation Problems in Stratified Sampling Under Box Constraints.” Advances in Statistical Analysis 96: 435-450. DOI: http://dx.doi.org/10.1007/s10182-011-0176-z.10.1007/s10182-011-0176-z
  35. Neyman, J. 1934. “On the Two Different Aspects of the Representative Method: The Method of Stratified Sampling and the Method of Purposive Selection.” Journal of the Royal Statistical Society 97: 558-625. DOI: http://dx.doi.org/10.2307/2342192.10.2307/2342192
  36. Pfeffermann, D. 1993. “The Role of Sampling Weights When Modeling Survey Data.” International Statistical Review 61: 317-337. DOI: http://dx.doi.org/10.2307/1403631.10.2307/1403631
  37. Pfeffermann, D., C.J. Skinner, D.J. Holmes, H. Goldstein, and J. Rasbash. 1998. “Weighting for Unequal Selection Probabilities in Multilevel Models.” Journal of the Royal Statistical Society Series B 60: 23-40. DOI: http://dx.doi.org/10.1111/1467-9868.00106.10.1111/1467-9868.00106
  38. Pfeffermann, D. and M. Sverchkov. 2007. “Small-Area Estimation Under Informative Probability Sampling of Areas and Within the Selected Areas.” Journal of the American Statistical Association 102: 1427-1439. DOI: http://dx.doi.org/10.1198/016214507000001094.10.1198/016214507000001094
  39. Pfeffermann, D. and M. Sverchkov. 2009. “Inference Under Informative Sampling.” In Handbook of Statistics, Vol. 29B, 455-487. New York: Elsevier.10.1016/S0169-7161(09)00239-9
  40. Prasad, N.G.N., and J.N.K. Rao. 1990. “The Estimation of the Mean Squared Error of Small Area Estimators.” Journal of the American Statistical Association 85: 163-171. DOI: http://dx.doi.org/10.1080/01621459.1990.10475320.10.1080/01621459.1990.10475320
  41. Rabe-Hesketh, S. and A. Skrondal. 2006. “Multilevel Modelling of Complex Survey Data.” Journal of the Royal Statistical Society: Series A (Statistics in Society) 169: 805-827. DOI: http://dx.doi.org/10.1111/j.1467-985X.2006.00426.x.10.1111/j.1467-985X.2006.00426.x
  42. Rao, J.N.K. 2003. Small Area Estimation. New York: John Wiley and Sons.10.1002/0471722189
  43. Särndal, C.-E., B. Swensson, and J. Wretman. 2003. Model Assisted Survey Sampling. New York: Springer.
  44. Schmid, T. 2012. “Spatial Robust Small Area Estimation applied on Business Data.” Ph.D. thesis, University of Trier.
  45. Shlomo, N. and R. Priam. 2013. “Improving Estimation in Business Surveys.” In BLUEETS Deliverable D6.2: Best practice recommendations on variance estimation and small area estimation in business surveys, edited by R. Bernardini Papalia, C. Bruch, T. Enderle, S. Falorsi, A. Fasulo, E. Fernandez-Vazquez, M. Ferrante, J.P. Kolb, R. Mu¨nnich, S. Pacei, R. Priam, P. Righi, T. Schmid, N. Shlomo, F. Volk, and T. Zimmermann, 52-70. Available at: http://www.blue-ets.istat.it/fileadmin/deliverables/Deliverable6.2.pdf (accessed October 16, 2014).
  46. Sinha, S.K. and J.N.K. Rao. 2009. “Robust Small Area Estimation.” Canadian Journal of Statistics 37(3): 381-399. ISSN 1708-945X.10.1002/cjs.10029
  47. Thompson, K.J. and B.E. Oliver. 2012. “Response Rates in Business Surveys: Going Beyond the Usual Performance Measure.” Journal of Official Statistics 28: 221-237.
  48. Tillé, Y. 2006. Sampling Algorithms. Springer Series in Statistics. New York: Springer.
  49. Torabi, M. and J.N.K. Rao. 2010. “Mean Squared Error Estimators of Small Area Means Using Survey Weights.” Canadian Journal of Statistics 38: 598-608.10.1002/cjs.10078
  50. Tschuprow, A. 1923. “On the Mathematical Expectation of the Moments of Frequency Distributions in the Case of Correlated Observations.” Metron 2: 461-493. Verret, F., M.A. Hidiroglou, and J.N.K. Rao. 2010. “Small Area Estimation Under Informative Sampling.” In Proceedings of the Survey Methods Section SSC Annual Meeting, May 2010.
  51. You, Y. and J.N.K. Rao. 2002. “A Pseudo-Empirical Best Linear Unbiased Prediction Approach to Small Area Estimation Using Survey Weights.” The Canadian Journal of Statistics 30: 431-439.10.2307/3316146
  52. You, Y. and J.N.K. Rao. 2003. “Pseudo Hierarchical Bayes Small Area Estimation Combining Unit Level Models and Survey Weights.” Journal of Statistical Planning and Inference 111: 197-208. DOI: http://dx.doi.org/10.1016/S0378-3758(02)00301-4. 10.1016/S0378-3758(02)00301-4
Language: English
Page range: 749 - 771
Submitted on: Jan 1, 2013
Accepted on: Jun 1, 2014
Published on: Dec 11, 2014
Published by: Sciendo
In partnership with: Paradigm Publishing Services
Publication frequency: 4 times per year

© 2014 Jan Pablo Burgard, Ralf Münnich, Thomas Zimmermann, published by Sciendo
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