Skip to main content

Advertisement

Springer Nature Link
Log in

Modified half-region depth for spatially dependent functional data

  • Original Paper
  • Published:
Stochastic Environmental Research and Risk Assessment Aims and scope Submit manuscript

Abstract

In this paper, we address the problem of getting order statistics for georeferenced functional data by means of depth functions. To reach this aim, we introduce the concept of spatial dispersion function for functional data in a specific location of the geographic space. Then we generalize the notion of modified half-region depth to spatial dispersion functions. Through the use of spatial dispersion functions we show how the data ordering criterion depends not only on the functional but also on the spatial component. The proposal is applied to two wide simulation studies and to real data coming from sensors.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

Explore related subjects

Discover the latest articles and news from researchers in related subjects, suggested using machine learning.

References

  • Albertos-Cuesta JA, Nieto-Rayes A (2008) The random Tukey depth. Comput Stat Data Anal 52(11):4979–4988

    Article  Google Scholar 

  • Balzanella A, Elvira R (2015) A depth function for geostatistical functional data. In: Morlini I, Minerva T, Vichi M (eds) Advances in statistical models for data analysis, Springer International Publishing, pp 9–16. doi:10.1007/978-3-319-17377-1_2

  • Bohorquez M, Giraldo R, Mateu J (2016) Optimal sampling for spatial prediction of functional data. Stat Methods Appl 25(1):3954

    Article  Google Scholar 

  • Bohorquez M, Giraldo R, Mateu J (2016) Multivariate functional random fields: prediction and optimal sampling. Stoch Environ Res Risk Assess 1–18. doi:10.1007/s00477-016-1266-y

  • Chakraborty A, Chaudhuri P (2014) On data depth in infinite dimensional spaces. Annal Inst Stat Math 66(2):303–324

    Article  Google Scholar 

  • Claeskens G, Hubert M, Slaets L, Vakili K (2014) Multivariate functional halfspace depth. J Am Stat Assoc 109:411–423

    Article  CAS  Google Scholar 

  • Cuevas A, Febrero M, Fraiman R (2007) Robust estimation and classification for functional data via projection-based depth notions. Comput Stat 22:481–496

    Article  Google Scholar 

  • Delicado P, Giraldo R, Comas C, Mateu J (2010) Statistics for spatial functional data: some recent contributions. Environmetric 21:224–239

    Article  Google Scholar 

  • Delicado P, Giraldo R, Comas C, Mateu J (2010) Spatial statistics for functional data: some recent contributions. Environmetrics 21:224–239

    Article  Google Scholar 

  • Dyckerhoff R (2002) Data depths satisfying the projection property. Adv Stat Anal 88:163–190

    Google Scholar 

  • Ferraty F, Vieu P (2006) Nonparametric functional data analysis theory and practice. Springer, New York

    Google Scholar 

  • Fraiman R, Muniz G (2001) Trimmed means for functional data. Test 10:419–440

    Article  Google Scholar 

  • Journel AG, Huijbregts Ch J (2004) Mining geostatistics. The Blackburn Press, Caldwell

    Google Scholar 

  • Liu R (1990) On a notion of data depth based on random simplices. Annal Stat 18:405–414

    Article  Google Scholar 

  • Lopez-Pintado S, Romo J (2009) On the concept of depth for functional data. J Am Stat Assoc 104:718–734

    Article  CAS  Google Scholar 

  • Lopez-Pintado S, Romo J (2011) A half-region depth for functional data. Comput Stat Data Anal 55(4):1679–1695

    Article  Google Scholar 

  • Mosler K (2002) Multivariate dispersion, central regions and depth: the Lift Zonoid approach. Springer, New York

    Book  Google Scholar 

  • Nieto-Reyes A, Battey H (2016) A topologically valid definition of depth for functional data. Stat Sci 31:61–79

    Article  Google Scholar 

  • Ramsay JO, Silverman BW (2005) Functional data analysis, 2nd edn. Springer, New York

    Google Scholar 

  • Romano E, Mateu J, Giraldo R (2015) On the performance of two clustering methods for spatial functional data. AStA Adv Stat Anal 99(4):467–492

    Article  Google Scholar 

  • Romano E, Balzanella A, Verde R (2016) Spatial variability clustering for spatially dependent functional data. Stat Comput 1–14. doi:10.1007/s11222-016-9645-2

  • Sun Y, Genton MG (2011) Functional boxplots. J Comput Graph Stat 20:316–334

    Article  Google Scholar 

  • Tukey J (1975) Mathematics and picturing data. In: Proceedings of the 1975 International Congress of Mathematics. 2, 523–531

  • Zuo Y, Serfling R (2000) General notions of statistical depth function. Annal Stat 28:461–482

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Second University of Naples, Caserta, Italy

    Antonio Balzanella, Elvira Romano & Rosanna Verde

Authors
  1. Antonio Balzanella
    View author publications

    Search author on:PubMed Google Scholar

  2. Elvira Romano
    View author publications

    Search author on:PubMed Google Scholar

  3. Rosanna Verde
    View author publications

    Search author on:PubMed Google Scholar

Corresponding author

Correspondence to Antonio Balzanella.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Balzanella, A., Romano, E. & Verde, R. Modified half-region depth for spatially dependent functional data. Stoch Environ Res Risk Assess 31, 87–103 (2017). https://doi.org/10.1007/s00477-016-1291-x

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00477-016-1291-x

Keywords

Profiles

  1. Antonio Balzanella View author profile
  2. Elvira Romano View author profile