On potentially negative space time covariances obtained as sum of products of marginal ones

Annals of the Institute of Statistical Mathematics

Volumn 60, Issue 4, 2008, Pages 865-882

  Gregori, P ^a   Porcu, E ^a   Mateu, J ^a   Sasvari Z ^b  

^a UNIVERSITAT JAUME I   (Spain)

^b DRESDEN UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Generalised product sum model; Geostatistics; Nonseparability; Separability; Space time covariance functions

Indexed keywords

EID: 55449138455     PISSN: 00203157     EISSN: 15729052     Source Type: Journal    
DOI: 10.1007/s10463-007-0122-8     Document Type: Article

References (33)

1. G.D. Anderson S.-L. Qiu 1997 A monotonicity property of the gamma function Proceedings of the American Mathematical Society 125 3355 3362
2. Berg C., Forst G. (1975). Potential theory on locally compact abelian groups. New York, Springer
3. C. Berg H.L. Pedersen 2001 A completely monotone function related to the Gamma function Journal of Computational and Applied Mathematics 133 219 230
4. C. Berg 2004 Integral representation of some functions related to the Gamma function Mediterranean Journal of Mathematics 1 433 439
5. S. Bochner 1933 Monotone funktionen, Stieltjes integrale und harmonische analyse Mathematische Annalen 108 378 410
6. Chilès J.P., Delfiner P. (1999). Geostatistics: modelling spatial uncertainty. New York, Wiley
7. Christakos G. (2000). Modern spatiotemporal geostatistics. Oxford, Oxford University Press
8. N.A.C. Cressie C. Huang 1999 Classes of nonseparable, spatiotemporal stationary covariance functions Journal of the American Statistical Association 94 1330 1340
9. L. De Cesare D.E. Myers D. Posa 2000 Product-sum covariance for space-time modeling: an environmental application Environmetrics 12 11 23
10. L. De Cesare D.E. Myers D. Posa 2001 Estimating and modeling space-time correlation structures Statistics and Probability Letters 51 9 14
11. S. De Iaco D.E. Myers D. Posa 2001 Space-time analysis using a general product-sum model Statistics and Probability Letters 52 21 28
12. Dimitrakopoulos R., Luo X. (1994). Spatiotemporal modeling: covariances and ordinary Kriging system. In: Dimitrakopoulos R. (eds), Geostatistics for the next century (pp. 88-93). Kluwer Academic Publisher.
13. T. Gneiting 2002 Nonseparable, stationary covariance functions for space-time data Journal of the American Statistical Association 97 590 600
14. Janauer G.A. (2001). Is what has been measured of any direct relevance to the success of the macrophyte in its particular environment? In O. Ravera (Ed.), Scientific and legal aspects of biological monitoring in freshwater. Journal of Limnology, 60(Suppl. 1), 33-38
15. M.V. Ibáñez-Gual A. Simó 2004 Conditional and unconditional simulation of healthy patients' visual fields Biometrical Journal 46 404 419
16. S.J. Levinson J.M. Beall E.J. Powers R.D. Bengtson 1984 Space-time statistics of the turbulence in a Tokamak edge plasma Nuclear Fusion 24 527 540
17. C. Ma 2002 Spatio-temporal covariance functions generated by mixtures Mathematical Geology 34 965 974
18. C. Ma 2005 Linear combinations of space-time covariance functions and variograms IEEE Transactions on Signal Processing 53 857 864
19. C. Ma 2005 Spatio-temporal variograms and covariance models Advances in Applied Probability 37 706 725
20. Matérn B. (1986). Spatial variation, 2nd edn. Berlin, Springer
21. M. Mitchell M.G. Genton M. Gumpertz 2005 Testing for separability of space-time covariances Environmetrics 16 819 831
22. D. Myers A. Journel 1990 Variograms with zonal anisotropies and non-invertible kriging systems Mathematical Geology 22 779 785
23. J.W. Pomeroy B. Toth R.J. Granger N.R. Hedstrom R.L.H. Essery 2003 Variation in surface energetics during snowmelt in a subarctic mountain catchment Journal of Hydrometeorology 4 702 719
24. Porcu E., Saura F., Mateu J. (2007). New classes of covariance and spectral density functions for spatio-temporal modelling. Stochastic Environmental Research and Risk Assessment (in press).
25. Rohuani S., Hall T.J. (1989). Space-time Kriging of groundwater data. In: Armstrong M. (eds), Geostatistics Vol. 2. New York, Kluwer Academic Publishers, pp. 639-651
26. Sasvári Z. (1994). Positive definite and definitizable functions. Berlin, Akademie Verlag
27. I.J. Schoenberg 1938 Metric spaces and completely monotone functions Annals of Mathematics 39 811 841
28. I.P. Shkarofsky 1968 Generalized turbulence space-correlation and wave-number spectrum-function pairs Canadian Journal of Physics 46 2133 2140
29. A.V. Vecchia 1988 Estimation and model identification for continuous spatial processes Journal of the Royal Statistical Society B 20 370 373
30. Z.-W. Xu J. Wu W.-P. Huo Z.-S. Wu 2003 Temporal skewness of electromagnetic pulsed waves propagating through random media with embedded irregularity slab Chinese Physics Letters 20 370 373
31. Z.-W. Xu J. Wu Z.-S. Wu 2003 Statistical temporal behaviour of pulse wave propagation through continuous random media Waves Random Media 13 59 73
32. Yaglom A.M. (1987). Correlation theory of stationary and related random functions. New York, Springer
33. V. Yakhot S.A. Orszag Z.-S. She 1989 Space-time correlations in turbulence - Kinematical versus dynamical effects Physics of Fluids 1 184 186