Estimating the Singularity Function of a Gaussian Process with Applications

Scandinavian Journal of Statistics

Volumn 23, Issue 4, 1996, Pages 581-595

  Istas, Jacques ^a  

^a CEMAGREF   (France)

Author keywords

Diffusion; Gaussian process; Quadratic variations; Singularity function; Wavelets

Indexed keywords

EID: 0030494879     PISSN: 03036898     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (18)

1. Andersson, L., Hall, N., Jawerth, B. & Peters, G. (1993). Wavelets on closed subsets on the real line. In Topics in the theory and applications of wavelets (eds L. Schumaker & Glenn Webb), 1-60.
2. Benhenni, K. & Cambanis, S. (1992). Sampling designs for estimating integrals of stochastic processes. Ann. Statist. 20, 161-194.
3. Brugière, P. (1991). Estimation de la variance d'une diffusion. C.R. Acad. Sci. Paris, Sér. I 312, 999-1004.
4. Cohen, A., Daubechies, I., Jawerth, B. & Vial, P. (1992). Multiresolution analysis, wavelets and fast algorithms on the interval. C.R. Acad. Sci. Paris, Sér. I 316, 417-421.
5. Dacunha-Castelle, D. & Duflo, M. (1983). Probabilités et statistiques, Vol. 2. Masson, Paris.
6. Daubechies, I. (1988). Orthonormal bases of compactly supported wavelets. Commun. Pure Appl. Math. 41, 909-996.
7. Daubechies, I. (1992). Ten lectures on wavelets. Vol. 61. SIAM, Pennsylvania.
8. Genon-Catalot, V., Laredo, C. & Picard, D. (1992). Non-parametric estimation of the diffusion coefficient by wavelets method. Scand J. Statist. 19, 317-335.
9. Guyon, X. & Leon, J. (1989). Convergence en loi des h-variations d'un processus gaussien stationnaire. Ann. Inst. Poincaré 25, 265-282.
10. Ikeda, N. & Watanabe, S. (1989). Stochastic differential equations and diffusion processes. North-Holland, Amsterdam.
11. Istas, J. & Lang, G. (1994). Variations quadratiques et estimation de l'exposant de Holder local d'un processus gaussien. C.R. Acad. Sci. Paris, Sér. I 319, 201-206.
12. Kerkyacharian, G. & Picard, D. (1993). Density estimation by kernel and wavelet methods. Optimality of Besov spaces. Statist. Probab. Lett. 18, 327-336.
13. Luenberger, L. (1979). Introduction to dynamical system: theory and applications. Wiley, New York.
14. Meyer, Y. (1990). Ondelettes et opérateurs. Vol. 1. Hermann, Paris.
15. Sacks, J. & Ylvisaker, D. (1966). Designs for regression problem problems with correlated errors. Ann. Math. Statist. 37, 66-89.
16. Sacks, J. & Ylvisaker, D. (1968). Designs for regression problem problems with correlated errors II. Ann. Math. Statist. 39, 49-69.
17. Sacks, J. & Ylvisaker, D. (1970). Designs for regression problem problems with correlated errors III. Ann. Math. Statist. 41, 2057-2074.
18. Soulier, P. (1991). Deviation quadratique pour des estimateurs de la variance d'une diffusion. C.R. Acad. Sci. Paris, Sér. I, 313, 783-786.