Parameter estimation for fractional Brownian surfaces

Statistica Sinica

Volumn 12, Issue 3, 2002, Pages 863-883

  Zhu, Zhengyuan ^a   Stein, Michael L ^a  

^a UNIVERSITY OF CHICAGO   (United States)

Author keywords

Fractal; Fractional Gaussian random field; Generalized least squares; REML; Self similar; Variogram

Indexed keywords

EID: 0036660803     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (12)

1. Chan, G. and Wood, A.T.A. (2000). Increment-based estimators of fractal dimension for two-dimensional surface data. Statist. Sinica 10, 343-376.
2. Constantine, A.G. and Hall, P. (1994). Characterizing surface smoothness via estimation of effective fractal dimension. J. Roy. Statist. Soc. Ser. B 56, 97-113.
3. Cressie, N. (1993). Statistics for Spatial Data (revised ed). John Wiley, New York.
4. Davies, S. and Hall, P. (1999). Fractal analysis of surface roughness by using spatial data. J. Roy. Statist. Soc. Ser. B 61, 3-37.
5. Kent, J.T. and Wood A.T.A. (1997). Estimating the fractal dimension of a locally self-similar Gaussian process by using increments. J. Roy. Statist. Soc. Set. B 59, 679-699.
6. Peitgen, H.O. and Saupe, D. (1988). The Science of Fractal Images. Springer-Verlag, New York.
7. Stein, M.L. (1995). Fixed-domain asymptotics for spatial periodograms. J. Amer. Statist. Assoc. 90, 1277-1288.
8. Stein, M.L. (1999). Interpolation of Spatial Data: Some Theory for Kriging. Springer-Verlag, New York.
9. Stein, M.L. (2002). Fast and exact simulation of fractional Brownian surfaces. J. Comput. Graphical Statist. In press.
10. Taylor, C.C. and Taylor, S.J. (1991). Estimating the dimension of a fractal. J. Roy. Statist. Soc. Set. B 53, 353-364.
11. Wilson, T.H. (2000). Some distinctions between self-similar and self-affine estimates of fractal dimension with case history. Math. Geology 32, 319-335.
12. Zhu, Z. and Stein, M.L. (2001). Parameter estimation for fractional Brownian surfaces. Uni-versity of Chicago, Department of Statistics technical report 501.