Likelihood-based confidence bands for fault lines in response surfaces

Probability Theory and Related Fields

Volumn 124, Issue 1, 2002, Pages 26-49

  Hall, Peter ^a,b   Rau, Christian ^a  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

^b CSIRO   (Australia)

Author keywords

Boundary estimation; Change point; Edge detection; Frontier analysis; Gaussian process with quadratic drift; Image analysis; Jump; Kernel methods; Least squares; Locally parametric methods; Multivariate confidence bands; Response surface; Smoothing

Indexed keywords

EID: 0036026178     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004400100195     Document Type: Article

References (27)

1. Adler, R.J.: An Introduction to Continuity, Extrema, and Related Topics for General Gaussian Processes. Institute of Mathematical Statistics Lecture Note Series 12. Institute of Mathematical Statistics, Hayward, CA (1990)
2. Alt, H., Godau, M.: Computing the Frechèt distance between two polygonal curves. Int. J. of Computational Geometry and Applications 5, 75-91 (1995)
3. Carlstein, E., Müller, H.-G., Siegmund, D.: Change-Point Problems. Institute of Mathematical Statistics Lecture Note Series 23. Institute of Mathematical Statistics, Hayward, CA (1994)
4. Deprins, D., Simar, L., Tulkens, H.: Measuring labor inefficiency in post offices. In The Performance of Public Enterprises: Concepts and measurements, eds. M. Marchand, P. Pestieau and H. Tulkens, 243-267. Amsterdam: North-Holland, 1984
5. Do Carmo, M. P.: Differential Geometry of Curves and Surfaces. Prentice-Hall Inc., Englewood Cliffs, NJ (1976)
6. Gasser, T. Kneip, A., Köhler, W.: A flexible and fast method for automatic smoothing. J. Amer. Statist. Assoc. 86, 643-652 (1991)
7. Gijbels, I., Mammen, E., Park, B.U., Simar, L.: On estimation of monotone and concave frontier functions. J. Amer. Statist. Assoc. 94, 220-228 (1999)
8. Groeneboom, P., Wellner, J.A.: Computing Chernoff's distribution. J. Comput. Graph. Statist. 10, 388-400 (2001)
9. Hall, P., Peng, L., Rau, C.: Local-likelihood tracking of fault lines and boundaries. J. R. Statist. Soc. B 63, 569-582 (2001)
10. Hall, P., Raimondo, M.: Approximating a line thrown at random onto a grid. Ann. Appl. Probab. 7, 648-665 (1997)
11. Hall, P., Raimondo, M.: On global performance of approximations to smooth curves using gridded data. Ann. Statist. 26, 2206-2217 (1998)
12. Hall, P., Rau, C.: Tracking a smooth fault line in a regression surface. Ann. Stat. 28, 713-733 (2000)
13. Haralick, R.M.: Ridges and valleys on digital images. Computer Graphics and Image Process. 22, 28-38 (1983)
14. Herrmann, E.: Local bandwidth choice in kernel regression. J. Comput. Graph. Statist. 6, 35-54 (1997)
15. Hoffman-Jørgensen, J.: Stochastic Processes on Polish Spaces. Various Publication Series 39. Aarhus Universitet, Aarhus, Denmark (1991)
16. Ivanoff, G., Merzbach, E.: Set-Indexed Martingales. Chapman and Hall/CRC, Boca Raton, FL (2000)
17. Kim, J., Pollard, D.: Cube root asymptotics. Ann. Stat. 18, 191-219 (1990)
18. Korostelev, A.P., Tsybakov, A.B.: Minimax Theory of Image Reconstruction. Springer Lecture Notes in Statistics 82. Berlin: Springer-Verlag, 1993
19. Mammen, E., Tsybakov, A.B.: Asymptotical minimax recovery of sets with smooth boundaries. Ann. Statist. 23, 502-524 (1995)
20. Marcel, B., Cattoen, M.: Edge and line detection in low level analysis. In Third Workshop on Electronic Control and Measuring Systems, 89-97. Université Paul Sabatier, Toulouse (1997)
21. Marron, J.S., Tsybakov, A.B.: Visual error criteria for qualitative smoothing. J. Amer. Statist. Assoc. 90, 499-507 (1995)
22. Müller, H.-G., Song, K.S.: A set-indexed process in a two-region image. Stoch. Proc. Appl. 62, 87-101 (1996)
23. Qiu, P.: Discontinuous regression surfaces fitting. Ann. Statist. 26, 2218-2245 (1998)
24. Qiu; P., Yandell, B.: Jump detection in regression surfaces. J. Computat. Graph. Statist. 6, 332-354 (1997)
25. Rudemo, M., Stryhn, H.: Approximating the distribution of maximum likelihood contour estimators in two-region images. Scand. J. Statist. 21, 41-55 (1994)
26. Seiford, L.M.: Data envelopment analysis: the evolution of the state-of-the-art (1978-1995). J. Productivity Anal. 7, 99-138 (1996)
27. van der Vaart, A.W., Wellner, J.A.: Weak Convergence and Empirical Processes. New York: Springer, 1996