Skip to main content
SpringerLink
Log in

Spatial Sampling Designs

  • Chapter
  • First Online:
Sampling Spatial Units for Agricultural Surveys

Part of the book series: Advances in Spatial Science ((ADVSPATIAL))

  • 1044 Accesses

Abstract

Geographically distributed observations have characteristics and peculiarities that should be appropriately considered when we are designing a survey. In fact, traditional sampling designs may be inadequate when investigating geo-coded data, because they do not capture any spatial homogeneity that may be present. The presence of this spatial effect may be inherent to the phenomenon under investigation, so it is desirable and appropriate that we consider this information in the sampling design.

In this chapter we discuss the main spatial sampling designs, also with applications, that have been recently introduced in literature.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    The kernel of a matrix A, is the set of all vectors x for which Ax = 0.

  2. 2.

    The empirical results presented here are partly based on Benedetti et al. (2015).

References

  • Arbia G (1993) The use of GIS in spatial statistical surveys. Int Stat Rev 61:339–359

    Article  Google Scholar 

  • Barabesi L, Franceschi S (2011) Sampling properties of spatial total estimators under tessellation stratified designs. Environmetrics 22:271–278

    Article  Google Scholar 

  • Bee M, Benedetti R, Espa G, Piersimoni F (2010) On the use of auxiliary variables in agricultural surveys design. In: Benedetti R, Bee M, Espa G, Piersimoni F (eds) Agricultural survey methods. Wiley, Chichester, pp 107–132

    Chapter  Google Scholar 

  • Benedetti R, Palma D (1995) Optimal sampling designs for dependent spatial units. Environmetrics 6:101–114

    Article  Google Scholar 

  • Benedetti R, Piersimoni F, Postiglione P (2015) Sampling spatial units: a comparison between different designs

    Google Scholar 

  • Berger YG (2004) A simple variance estimator for unequal probability sampling without replacement. J Appl Stat 31:305–315

    Article  Google Scholar 

  • Bondesson L, Grafström A (2011) An extension of Sampford’s method for unequal probability sampling. Scand J Stat 38:377–392

    Article  Google Scholar 

  • Bondesson L, Thorburn D (2008) A list sequential sampling method suitable for real-time sampling. Scand J Stat 35:466–483

    Article  Google Scholar 

  • Breidt FJ, Chauvet G (2012) Penalized balanced sampling. Biometrika 99:945–958

    Article  Google Scholar 

  • Chauvet G (2009) Stratified balanced sampling. Surv Methodol 35:115–119

    Google Scholar 

  • Chauvet G, Tillé Y (2006) A fast algorithm of balanced sampling. Comput Stat 21:53–62

    Article  Google Scholar 

  • Chauvet G, Bonnéry D, Deville JC (2011) Optimal inclusion probabilities for balanced sampling. J Stat Plan Inference 141:984–994

    Article  Google Scholar 

  • Christman MC (2000) A review of quadrat-based sampling of rare, geographically clustered populations. J Agric Biol Environ Stat 5:168–201

    Article  Google Scholar 

  • Colbourn CJ, Ling ACH (1998) A class of partial triple systems with applications in survey sampling. Commun Stat Theory Methods 27:1009–1018

    Article  Google Scholar 

  • Colbourn CJ, Ling ACH (1999) Balanced sampling plans with block size four excluding contiguous units. Aust J Comb 20:37–46

    Google Scholar 

  • Cordy C (1993) An extension of the Horvitz–Thompson theorem to point sampling from a continuous universe. Stat Probab Lett 18:353–362

    Article  Google Scholar 

  • Cressie N (1993) Statistics for spatial data. Wiley, New York

    Google Scholar 

  • Dalenius T, Hájek J, Zubrzycki S (1961) On plane sampling and related geometrical problems. In: Proceedings of the 4th Berkeley symposium on probability and mathematical statistics, vol 1, pp 125–150

    Google Scholar 

  • Das AC (1950) Two-dimensional systematic sampling and the associated stratified and random sampling. Sankhya 10:95–108

    Google Scholar 

  • Delmelle EM (2013) Spatial sampling. In: Fischer MM, Nijkamp P (eds) Handbook of regional science. Springer, Berlin, pp 1385–1399

    Google Scholar 

  • Deville JC, Tillé Y (1998) Unequal probability sampling without replacement through a splitting method. Biometrika 85:89–101

    Article  Google Scholar 

  • Deville JC, Tillé Y (2004) Efficient balanced sampling: the cube method. Biometrika 91:893–912

    Article  Google Scholar 

  • Deville JC, Tillé Y (2005) Variance approximation under balanced sampling. J Stat Plan Inference 128:411–425

    Article  Google Scholar 

  • Dunn R, Harrison A (1993) Two-dimensional systematic sampling of land use. Appl Stat 42:585–601

    Article  Google Scholar 

  • Everitt BS, Landau S, Leese M, Stahl D (2011) Cluster analysis. Wiley, Chichester

    Book  Google Scholar 

  • Fattorini L (2006) Applying the Horvitz–Thompson criterion in complex designs: a computer-intensive perspective for estimating inclusion probabilities. Biometrika 93:269–278

    Article  Google Scholar 

  • Fattorini L (2009) An adaptive algorithm for estimating inclusion probabilities and performing the Horvitz–Thompson criterion in complex designs. Comput Stat 24:623–639

    Article  Google Scholar 

  • Fuller WA (2009) Some design properties of a rejective sampling procedure. Biometrika 96:933–944

    Article  Google Scholar 

  • Grafström A (2010a) On a generalization of Poisson sampling. J Stat Plan Inference 140:982–991

    Article  Google Scholar 

  • Grafström A (2010b) Entropy of unequal probability sampling designs. Stat Meth 7:84–97

    Article  Google Scholar 

  • Grafström A (2012) Spatially correlated Poisson sampling. J Stat Plan Inference 142:139–147

    Article  Google Scholar 

  • Grafström A, Lundström NLP (2013) Why well spread probability samples are balanced. Open J Stat 3:36–41

    Article  Google Scholar 

  • Grafström A, Schelin L (2014) How to select representative samples. Scand J Stat 41:277–290

    Article  Google Scholar 

  • Grafström A, Tillé Y (2013) Doubly balanced spatial sampling with spreading and restitution of auxiliary totals. Environmetrics 24:120–131

    Article  Google Scholar 

  • Grafström A, Lundström NLP, Schelin L (2012) Spatially balanced sampling through the pivotal method. Biometrics 68:514–520

    Article  Google Scholar 

  • Hastie T, Tibshirani R (1990) Generalized additive models. Chapman and Hall, London

    Google Scholar 

  • Hedayat A, Stufken J (1998) Sampling designs to control selection probabilities of contiguous units. J Stat Plan Inference 72:333–345

    Article  Google Scholar 

  • Hedayat A, Rao CR, Stufken J (1988a) Sampling designs excluding contiguous units. J Stat Plan Inference 19:159–170

    Article  Google Scholar 

  • Hedayat A, Rao CR, Stufken J (1988b) Designs for survey sampling avoiding contiguous units. In: Krishnaiah PR, Rao CR (eds) Handbook of statistics, vol 6, Sampling. Elsevier, The Netherlands, pp 575–583

    Google Scholar 

  • Knottnerus P (2003) Sample survey theory: some Pythagorean perspectives. Springer, New York

    Google Scholar 

  • Lantuejoul C (2002) Geostatistical simulation. Springer, New York

    Book  Google Scholar 

  • Larsen DP, Kincaid TM, Jacobs SE, Urquhart NS (2001) Designs for evaluating local and regional scale trends. Bioscience 51:1049–1058

    Article  Google Scholar 

  • Mandal B, Parsad R, Gupta V (2008) IPPS Sampling plans excluding adjacent units. Comm Stat Theor Meth 3:2532–2550

    Article  Google Scholar 

  • Mandal B, Parsad R, Gupta V, Sud U (2009) A family of distance balanced sampling plans. J Stat Plan Inference 139:860–874

    Article  Google Scholar 

  • Mark DM (1990) Neighbor-based properties of some orderings of two-dimensional space. Geogr Anal 2:145–157

    Google Scholar 

  • Murthy MN (1957) Ordered and unordered estimators in sampling without replacement. Sankhya 18:379–390

    Google Scholar 

  • Neyman J (1934) On the two different aspects of representative method: the method of stratified sampling and the method of purposive selection. J R Stat Soc 97:558–606

    Article  Google Scholar 

  • Olea RA (1984) Sampling design optimization for spatial functions. Math Geol 16:369–392

    Article  Google Scholar 

  • Overton WS, Stehman SV (1993) Properties of designs for sampling continuous spatial resources from a triangular grid. Commun Stat Theory Methods 22:2641–2660

    Google Scholar 

  • Raj D (1956) Some estimators in sampling with varying probabilities without replacement. J Am Stat Assoc 51:269–284

    Article  Google Scholar 

  • Ripley BD (1981) Spatial statistics. Wiley, New York

    Google Scholar 

  • Robertson BL, Brown JA, McDonald T, Jaksons P (2013) BAS: balanced acceptance sampling of natural resources. Biometrics 69:776–784

    Article  Google Scholar 

  • Rogerson P, Delmelle E (2004) Optimal sampling design for variables with varying spatial importance. Geogr Anal 36:177–194

    Article  Google Scholar 

  • Royall RM (1976a) Likelihood functions in finite population sampling theory. Biometrika 63:605–614

    Article  Google Scholar 

  • Royall RM (1976b) The linear least squares prediction approach to two-stage sampling. J Am Stat Assoc 71:657–664

    Article  Google Scholar 

  • Royall RM, Herson JH (1973) Robust estimation in finite populations I. J Am Stat Assoc 68:880–889

    Article  Google Scholar 

  • Salehi MM (2004) Optimal sampling design under a spatial correlation model. J Stat Plan Inference 118:9–18

    Article  Google Scholar 

  • Salvati N, Tzavidis N, Pratesi M, Chambers RL (2010) Small area estimation via M-quantile geographically weighted regression. Test 19:1–28

    Article  Google Scholar 

  • Sampford MR (1967) On sampling without replacement with unequal probabilities of selection. Biometrika 54:499–513

    Article  Google Scholar 

  • Särndal CE, Swensson B, Wretman J (1992) Model assisted survey sampling. Springer, New York

    Google Scholar 

  • Stevens DL Jr (1997) Variable density grid-based sampling designs for continuous spatial population. Environmetrics 8:167–195

    Article  Google Scholar 

  • Stevens DL Jr, Olsen AR (1999) Spatially restricted surveys over time for aquatic resources. J Agric Biol Environ Stat 4:415–428

    Article  Google Scholar 

  • Stevens DL Jr, Olsen AR (2003) Variance estimation for spatially balanced samples of environmental resources. Environmetrics 14:593–610

    Article  Google Scholar 

  • Stevens DL Jr, Olsen AR (2004) Spatially balanced sampling of natural resources. J Am Stat Assoc 99:262–278

    Article  Google Scholar 

  • Stufken J (1993) Combinatorial and statistical aspects of sampling plans to avoid the selection of adjacent units. J Comb Inf Syst Sci 18:81–92

    Google Scholar 

  • Stufken J, Wright JH (2001) Polygonal designs with blocks of size k < 10. Metrika 54:179–184

    Article  Google Scholar 

  • Stufken J, Song SY, See K, Driessel KR (1999) Polygonal designs: some existence and non-existence results. J Stat Plan Inference 77:155–166

    Article  Google Scholar 

  • Tillé Y (2006) Sampling algorithms. Springer series in statistics. Springer, New York

    Google Scholar 

  • Tillé Y (2011) Ten years of balanced sampling with the cube method: an appraisal. Surv Methodol 37:215–226

    Google Scholar 

  • Tillé Y, Favre AC (2005) Optimal allocation in balanced sampling. Stat Probab Lett 74:31–37

    Article  Google Scholar 

  • Valliant R, Dorfman AH, Royall RM (2000) Finite population sampling and inference: a prediction approach. Wiley, New York

    Google Scholar 

  • Waagepetersen R (2007) An estimating function approach to inference for inhomogeneous Neyman-Scott processes. Biometrics 63:252–258

    Article  Google Scholar 

  • Wang JF, Stein A, Gao BB, Ge Y (2012) A review of spatial sampling. Spat Stat 2:1–14

    Article  Google Scholar 

  • Wolter KM (2007) Introduction to variance estimation, 2nd edn. Springer, New York

    Google Scholar 

  • Wood SN (2006) Generalized additive models: an introduction with R. Chapman and Hall/CRC, Boca Raton, FL

    Google Scholar 

  • Wright J (2008) Two-dimensional balanced sampling plans excluding adjacent units. J Stat Plan Inference 138:145–153

    Article  Google Scholar 

  • Wright J, Stufken J (2008) New balanced sampling plans excluding adjacent units. J Stat Plan Inference 138:3326–3335

    Article  Google Scholar 

  • Yates F (1946) A review of recent statistical developments in sampling and sampling surveys. J R Stat Soc Ser A 109:12–43

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Economic Studies, “G. d’Annunzio” University of Chieti-Pescara, Pescara, Italy

    Roberto Benedetti & Paolo Postiglione

  2. Agricultural Statistical Service, Italian National Statistical Institute, ISTAT, Rome, Italy

    Federica Piersimoni

Authors
  1. Roberto Benedetti
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Federica Piersimoni
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Paolo Postiglione
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Benedetti, R., Piersimoni, F., Postiglione, P. (2015). Spatial Sampling Designs. In: Sampling Spatial Units for Agricultural Surveys. Advances in Spatial Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-46008-5_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-46008-5_7

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-46007-8

  • Online ISBN: 978-3-662-46008-5

  • eBook Packages: Business and EconomicsEconomics and Finance (R0)

Publish with us

Policies and ethics

Search

Navigation