Back
 OJS  Vol.4 No.5 , August 2014
The Use of Spatial Sampling Designs in Business Surveys
Maria Michela Dickson*, Roberto Benedetti, Diego Giuliani, Giuseppe Espa
Show more
Abstract: An innovative use of spatial sampling designs is here presented. Sampling methods which consider spatial locations of statistical units are already used in agricultural and environmental contexts, while they have never been exploited for establishment surveys. However, the rapidly increasing availability of geo- referenced information about business units makes that possible. In business studies, it may indeed be important to take into account the presence of spatial autocorrelation or spatial trends in the variables of interest, in order to have more precise and efficient estimates. The opportunity of using the most innovative spatial sampling designs in business surveys, in order to produce samples that are well spread in space, is here tested by means of Monte Carlo experiments. For all designs, the Horvitz-Thompson estimator of the population total is used both with equal and unequal inclusion probabilities. The efficiency of sampling designs is evaluated in terms of relative RMSE and efficiency gain compared with designs ignoring the spatial information. Furthermore, an evaluation of spatially balancing samples is also conducted.
Keywords: Spatial Sampling Design, Business Surveys, Horvitz-Thompson Estimator, Spatial Balance
Cite this paper: Dickson, M. , Benedetti, R. , Giuliani, D. and Espa, G. (2014) The Use of Spatial Sampling Designs in Business Surveys. Open Journal of Statistics, 4, 345-354. doi: 10.4236/ojs.2014.45034.
References

[1]   Arbia, G. (1993) The Use of GIS in Spatial Statistical Surveys. International Statistical Review, 61, 339-359.
http://dx.doi.org/10.2307/1403632

[2]   Grafström, A. (2012) Spatially Correlated Poisson Sampling. Journal of Statistical Planning and Inference, 142, 139-147. http://dx.doi.org/10.1016/j.jspi.2011.07.003

[3]   Grafström, A., Lundström, N.L.P. and Schelin, L. (2012) Spatially Balanced Sampling through the Pivotal Method. Biometrics, 68, 514-520.
http://dx.doi.org/10.1111/j.1541-0420.2011.01699.x

[4]   Deville, J.-C. and Tillé, Y. (2004) Efficient Balanced Sampling: The Cube Method. Biometrika, 91, 893-912.
http://dx.doi.org/10.1093/biomet/91.4.893

[5]   Grafström, A. and Tillé, Y. (2013) Doubly Spatial Sampling with Spreading and Restitution of Auxiliary Totals. Environmentrics, 24, 120-131.
http://dx.doi.org/10.1002/env.2194

[6]   Hedayat, A.S., Rao, C.R. and Stufken, J. (1988) Sampling Plans Excluding Contiguous Units. Journal of Statistical Planning and Inference, 19, 159-170.
http://dx.doi.org/10.1016/0378-3758(88)90070-5

[7]   Hedayat, A.S., Rao, C.R. and Stufken, J. (1988) Designs in Survey Sampling Avoiding Contiguous Units. In: Krishnaiah, P.R. and Rao, C.R., Eds., Handbook of Statistics, Vol. 6, Elsevier, Amsterdam, 575-583.

[8]   Wright, J.H. and Stufken, J. (2008) New Balanced Sampling Plans Excluding Adjacent Units. Journal of Statistical Planning and Inference, 138, 3326-3335.
http://dx.doi.org/10.1016/j.jspi.2006.10.020

[9]   Stevens Jr., D.L. and Olsen, A.R. (2004) Spatially Balanced Sampling of Natural Resources. Journal of the American Statistical Association, 99, 262-278.
http://dx.doi.org/10.1198/016214504000000250

[10]   Mark, D.M. (1990) Neighbor-Based Properties of Some Orderings of Two-Dimensional Space. Geographical Analysis, 2, 145-157.

[11]   Bondesson, L. and Thorburn, D. (2008) A List Sequential Sampling Method Suitable for Real-Time Sampling. Scandinavian Journal of Statistics, 35, 466-483.
http://dx.doi.org/10.1111/j.1467-9469.2008.00596.x

[12]   Grafström, A. (2010) Entropy of Unequal Probability Sampling Designs. Statistical Methodology, 7, 84-97.
http://dx.doi.org/10.1016/j.stamet.2009.10.005

[13]   Deville, J.-C. and Tillé, Y. (1998) Unequal Probability Sampling without Replacement through a Splitting Method. Biometrika, 85, 89-101.
http://dx.doi.org/10.1093/biomet/85.1.89

[14]   Yates, F. (1949) Sampling Methods for Census and Surveys. Griffin, London.

[15]   Royall, R. and Herson, J. (1973) Robust Estimation in Finite Populations I. Journal of the American Statistical Association, 68, 880-889.
http://dx.doi.org/10.1080/01621459.1973.10481440

[16]   Deville, J.-C., Grosbras, J.-M. and Roth, N. (1988) Efficient Sampling Algorithms and Balanced Sample. In: Payne, R. and Green, P., Eds., COMPSTAT, PhysicaVerlag, Heidelberg, 255-266.
http://dx.doi.org/10.1007/978-3-642-46900-8_35

[17]   Hedayat, A. and Majumdar, D. (1995) Generating Desirable Sampling Plans by the Technique of Trade-Off in Experimental Design. Journal of Statistical Planning and Inference, 44, 237-247.
http://dx.doi.org/10.1016/0378-3758(94)00044-V

[18]   Breidt, F.J. and Chauvet, G. (2012) Penalized Balanced Sampling. Biometrika, 99, 945-958.
http://dx.doi.org/10.1093/biomet/ass033

[19]   Tillé, Y. (2006) Sampling Algorithms. Springer, New York.

[20]   Council Regulation (EEC) No 696/93 of 15 March 1993 on the Statistical Units for the Observation and Analysis of the Production System in the Community.
http://eur-lex.europa.eu/LexUriServ/LexUriServ.do?uri=CELEX:31993R0696:EN:HTML

[21]   Horvitz, D.G. and Thompson, D.J. (1952) A Generalization of Sampling without Replacement from a Finite Universe. Journal of the American Statistical Association, 47, 663-685.

[22]   Grafström, A. (2014) Balanced Sampling: Balanced and Spatially Balanced Sampling. R Package Version 1.4.
http://www.antongrafstrom.se/balancedsampling

[23]   Grafström, A. and Lundström, N.L.P. (2013) Why Well Spread Probability Samples Are Balanced. Open Journal of Statistics, 3, 36-41.
http://dx.doi.org/10.4236/ojs.2013.31005

 
 
Top