Minimax estimation of the diffusion coefficient through irregular samplings

Statistics and Probability Letters

Volumn 32, Issue 1, 1997, Pages 11-24

  Hoffmann, Marc ^a  

^a CNRS   (France)

Author keywords

Besov spaces; Diffusion processes; Irregular sampling schemes; Minimax estimation; Wavelet orthonormal bases; Wavelets on the interval

Indexed keywords

EID: 0031566894     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0167-7152(96)00052-1     Document Type: Article

References (16)

1. Cohen, A., I. Daubechies and P. Vial (1994), Wavelets on the interval and fast wavelet transform, Appl. Comput. Harm. Anal. 1, 54-81.
2. Donhal, G. (1987), On estimating the diffusion coefficient, J. Appl. Probab. 24, 105-114.
3. Donoho, D.L., I.M. Johnstone, G. Kerkyacharian and D. Picard (1995), Density estimation by wavelet thresholding, Ann. Statist., to appear.
4. Dorogovcev, A.Ja. (1976), The consistency of an estimate of a parameter of a stochastic differential equation, Theoret. Probab. Math. Statist. 10, 73-82.
5. Florens-Zmirou, D. (1993), On estimating the diffusion coefficient from discrete observations, J. Appl. Probab. 30, 790-804.
6. Genon-Catalot, V. and J. Jacod (1993), On the estimation of the diffusion coefficient for multidimensional diffusion processes, Ann. Inst. H. Poincaré 29, 119-151.
7. Genon-Catalot, V. and J. Jacod (1994), On the estimation of the diffusion coefficient for diffusion processes: random samplings, Scand. J. Statist. 21, 193-221.
8. Genon-Catalot, V., C. Laredo and D. Picard (1992), Nonparametric estimation of the diffusion coefficient by wavelets methods, Scand. J. Statist. 19, 319-335.
9. Ibragimov, I.A. and R.Z. Has'minski (1981), Statistical Estimation, Asymptotic Theory (Springer, Berlin).
10. Jacod, J. (1993), Random sampling in estimation problems for continuous Gaussian processes with independent increments, Stochastic Process. Appl. 44, 181-204.
11. Kerkyacharian, G. and D. Picard (1992), Density estimation in Besov spaces, Statist. Probab. Lett. 13, 15-24.
12. Kerkyacharian, G. and D. Picard (1993), Density estimation by kernel and wavelets methods: Optimality of Besov Spaces, Statist. Probab. Lett. 18, 327-336.
13. Meyer, Y. (1990), Ondelettes et Opérateurs I (Hermann, Paris).
14. Revuz, D. and M. Yor (1991), Continuous martingales and Brownian motion (Springer, Berlin).
15. Petrov, V.V. (1992), Generalizations of Rosenthal's inequalities, Ann. Acad. Sci. Fennicae (A) 17, 117-121.
16. Soulier, P. (1993), Thèse, Université Paris 11, Orsay.