Goodness-of-fit tests for the spatial spectral density

Stochastic Environmental Research and Risk Assessment

Volumn 24, Issue 1, 2010, Pages 67-79

  Crujeiras, Rosa M ^a   Fernández Casal, Rubén ^b   González Manteiga, Wenceslao ^a  

^a UNIVERSITY OF SANTIAGO DE COMPOSTELA   (Spain)

^b UNIVERSITY OF A CORUÑA   (Spain)

Author keywords

Goodness of fit tests; Kernel estimators; Local likelihood; Spatial spectral density

Indexed keywords

GENERALIZED LIKELIHOOD RATIO TEST; GOODNESS-OF-FIT TEST; GOODNESS-OF-FIT TESTING; KERNEL ESTIMATORS; LOCAL LIKELIHOOD; LOG-PERIODOGRAM; NULL HYPOTHESIS; PERIODOGRAMS; REGRESSION MODEL; RESAMPLING; SIMULATION STUDIES; SPATIAL CORRELATIONS; SPATIAL DATA ANALYSIS;

ESTIMATION; MAXIMUM LIKELIHOOD ESTIMATION; NORMAL DISTRIBUTION; REGRESSION ANALYSIS; STATISTICAL TESTS;

SPECTRAL DENSITY;

CORRELATION; DETECTION METHOD; ESTIMATION METHOD; MODELING; SIMULATION; SPATIAL ANALYSIS; TESTING METHOD;

EID: 77949775930     PISSN: 14363240     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00477-008-0300-0     Document Type: Article

References (36)

1. Alonso FJ, Angulo JM, Bueso MC (1996) Estimation and smoothing from incomplete data for a class of lattice processes. Comm Stat Theory Methods 25: 667-681.
2. Besag JE (1974) Spatial interaction and the statistical analysis of lattice systems. J R Stat Soc Ser B 36: 192-236.
3. Brilinger DR (1974) Fourier analysis of stationary processes. Proc IEEE 62: 1628-1643.
4. Brilinger DR (1981) Time series. Data analysis and theory. Holden-Day, Oakland.
5. González-Manteiga W, Cao R (1993) Testing the hypothesis of a general linear model using nonparametric regression estimation. Test 2: 161-188.
6. Chilès JP, Delfiner P (1999) Geostatistics. Wiley, New York.
7. Cressie N (1993) Statistics for spatial data. Wiley-Interscience, New York.
8. Crujeiras RM, Fernández-Casal R (2009) On the estimation of the spectral density of continuous spatial processes. Statistics (in press).
9. Crujeiras RM, Fernández-Casal R, González-Manteiga W (2007) Goodness-of-fit tests for the spatial spectral density. Technical report. Department of Statistics and Operations Research. http://eio. usc. es/pub/reports. html.
10. Dahlhaus R, Künsch H (2000) Edge effects and efficient parameter estimation for stationary random fields. Biometrika 74: 877-882.
11. Dahlhaus R, Wefelmeyer W (1996) Asimptotically optimal estimation in misspecified times series models. Ann Stat 24: 952-974.
12. de Jong P (1987) A central limit theorem for generalized quadratic forms. Prob Theory Relat Fields 75: 261-277.
13. Diblasi A, Bowman AW (2001) On the use of the variogram in checking for independence in spatial data. Biometrics 57: 211-218.
14. Fan J, Zhang W (2004) Generalised likelihood ratio tests for spectral density. Biometrika 91: 195-209.
15. Fan J, Zhang C, Zhang J (2001) Generalized likelihood ratio statistics and Wilks phenomenon. Ann Stat 29: 153-193.
16. Fuentes M (2002) Spectral methods for nonstationary spatial processes. Biometrika 89: 197-210.
17. García-Soidán PH, Febrero-Bande F, González-Manteiga W (2004a) Local linear regression estimation of the semivariogram. Stat Prob Lett 64: 169-179.
18. García-Soidán PH, Febrero-Bande F, González-Manteiga W (2004b) Nonparametric kernel estimation of an isotropic variogram. J Stat Plan Infer 121: 65-92.
19. Goldberg D (1989) Genetic algorithms in search, optimization and machine learning. Addison-Wesley, Reading.
20. Guyon X (1982) Parameter estimation for a stationary process on a d-dimensional lattice. Biometrika 69: 95-105.
21. Härdle W, Mammen E (1993) Comparing nonparametric versus parametric regression fits. Ann Stat 21: 1926-1947.
22. Hart JD (1997) Nonparametric smoothing and lack-of-fit tests. Springer. New York.
23. Maglione D, Diblasi A (2004) Exploring a valid model for the variogram of an isotropic spatial process. Stoch Environ Res Risk Assess 18: 366-376.
24. Martin RJ (1979) A subclass of lattice processes applied to a problem in planar sampling. Biometrika 66: 209-217.
25. McBratney AB, Webster R (1981) Detection of ridge and furrow pattern by spectral analysis of crop yield. Int Stat Rev 49: 45-52.
26. Paparoditis E (2000) Spectral density based goodness-of-fit tests for time series models. Scand J Stat 27: 143-176.
27. Porcu E, Crujeiras RM, Mateu J, González-Manteiga W (2009) On the second order properties of the multidimensional periodogram for regularly spaced data. Theory Prob Appl (SIAM) (in press).
28. Priestley MB (2000) Spectral analysis and time series. Academic Press, London.
29. Robinson P (2007) Nonparametric spectrum estimation for spatial data. J Stat Plan Inference 137: 1024-1034.
30. Stute W (1997) Nonparametric model checks for regression. Ann Stat 25: 613-641.
31. Stute W, González Manteiga W, Presedo Quindimil M (1998) Bootstrap approximations in model checks for regression. J Am Stat Assoc 93: 141-149.
32. Whittle P (1954) On stationary processes in the plane. Biometrika 41: 434-449.
33. Yaglom AM (1987) Correlation theory of stationary and related random functions. Springer Series in Statistics. New York.
34. Young LJ, Young JH (1998) Statistical ecology. Kluwer, Dordrecht.
35. Zhang C, Dette H (2004) A power comparison between nonparametric regression tests. Stat Prob Lett 66: 289-301.
36. Zheng JX (1996) A consistent test of functional form via nonparametric estimation techniques. Journal of Econometrics 75: 263-289.