Finite area smoothing with generalized distance splines

Environmental and Ecological Statistics

Volumn 21, Issue 4, 2014, Pages 715-731

  Miller, David L ^a   Wood, Simon N ^b  

^a UNIVERSITY OF ST ANDREWS   (United Kingdom)

^b University of Bath   (United Kingdom)

Author keywords

Finite area smoothing; Generalized additive model; Multidimensional scaling; Spatial modelling; Splines

Indexed keywords

FINITE ELEMENT METHOD; NUMERICAL MODEL; SMOOTHING; SPATIAL ANALYSIS; STATISTICAL ANALYSIS;

EID: 84911987601     PISSN: 13528505     EISSN: 15733009     Source Type: Journal    
DOI: 10.1007/s10651-014-0277-4     Document Type: Article

References (27)

1. Augustin N, Musio M, von Wilpert K, Kublin E, Wood SN, Schumacher M (2009) Modeling spatiotemporal forest health monitoring data. J Am Stat Assoc 104(487):899–911
2. Bernstein M, De Silva V, Langford J, Tenenbaum J (2000) Graph approximations to geodesics on embedded manifolds. Technical report, Department of Psychology, Stanford University. ftp://ftp-sop.inria.fr/prisme/boissonnat/ImageManifolds/isomap.pdf
3. Chatfield C, Collins AJ (1980) Introduction to multivariate analysis. Science paperbacks, Chapman and Hall
4. Curriero F (2005) On the use of non-euclidean isotropy in geostatistics. Technical report 94, Johns Hopkins University, Department of Biostatistics. http://www.bepress.com/cgi/viewcontent.cgi?article=1094&context=jhubiostat
5. Driscoll TA, Trefethen L (2002) Schwartz-Christoffel transform. Cambridge University Press, Cambridge
6. Duchon J (1977) Splines minimizing rotation-invariant semi-norms in Sobolev spaces. Constructive theory of functions of several variables, pp 85–100
7. Floyd RW (1962) Algorithm 97: shortest path. Commun. ACM 5(6):345–345
8. Gower J (1968) Adding a point to vector diagrams in multivariate analysis. Biometrika 55(3):582
9. Hastie TJ, Tibshirani RJ (1990) Generalized additive models. Monographs on statistics and applied probability. Taylor & Francis, New York
10. Higham NJ (1987) Computing real square roots of a real matrix. Linear Algebra Appl 88–89:405–430. doi:10.1016/0024-3795(87)90118-2
11. Jensen OP, Christman MC, Miller TJ (2006) Landscape-based geostatistics: a case study of the distribution of blue crab in Chesapeake Bay. Environmetrics 17(6):605–621. doi:10.1002/env.767
12. Løland A, Høst G (2003) Spatial covariance modelling in a complex coastal domain by multidimensional scaling. Environmetrics 14(3):307–321. doi:10.1002/env.588
13. Miller DL (2012) On smooth models for complex domains and distances. PhD thesis, University of Bath
14. Miller DL, Burt ML, Rexstad EA (2013) Spatial models for distance sampling data: recent developments and future directions. Methods in Ecology and Evolution
15. Oh MS, Raftery AE (2001) Bayesian multidimensional scaling and. J Am Stat Assoc 96(455):1031
16. Ramsay T (2002) Spline smoothing over difficult regions. J R Stat Soc Ser B Stat Methodol 64(2):307–319
17. Rue H, Held L (2005) Gaussian Markov random fields: theory and applications. Monographs on statistics and applied probability. Taylor & Francis, New York
18. Ruppert D, Wand M, Carroll RJ (2003) Semiparametric regression. Cambridge series on statistical and probabilistic mathematics. Cambridge University Press, Cambridge
19. Sampson PD, Guttorp P (1992) Nonparametric estimation of nonstationary spatial covariance structure. J Am Stat Assoc 87(417):108–119
20. Scott-Hayward LAS, MacKenzie ML, Donovan CR, Walker CG, Ashe E (2013) Complex region spatial smoother (CReSS). J Comput Graph. Stat. doi: 10.1080/10618600.2012.762920
21. Vretblad A (2003) Fourier analysis and its applications. Graduate texts in mathematics. Springer, Berlin
22. Wang H, Ranalli M (2007) Low-rank smoothing splines on complicated domains. Biometrics 63(1):209–217
23. Williams R, Hedley SL, Branch TA, Bravington MV, Zerbini AN, Findlay KP (2011) Chilean blue whales as a case study to illustrate methods to estimate abundance and evaluate conservation status of rare species. Conserv Biol 25(3):526–535. doi:10.1111/j.1523-1739.2011.01656.x
24. Wood SN (2003) Thin plate regression splines. J R Stat Soc Ser B Stat Methodol 65(1):95–114
25. Wood SN (2006) Generalized additive models: an introduction with R. Chapman & Hall/CRC, London
26. Wood SN (2011) Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models. J R Stat Soc Ser B Stat Methodol 73(1):3–36
27. Wood SN, Bravington MV, Hedley SL (2008) Soap film smoothing. J R Stat Soc Ser B Stat Methodol 70(5):931–955