Limit of the quadratic risk in density estimation using linear methods

Statistics and Probability Letters

Volumn 31, Issue 4, 1997, Pages 299-312

  Gérard, Kerkyacharian ^a   Dominique, Picard ^b  

^a UNIVERSITÉ DE PICARDIE JULES VERNE   (France)

^b UNIVERSITÉ PARIS DESCARTES   (France)

Author keywords

Besov spaces; Mean integrated squared error density estimation; Minimax estimation; Wavelet orthonormal bases

Indexed keywords

EID: 0031065256     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0167-7152(96)00044-2     Document Type: Article

References (20)

1. Bergh, J. and J. Löfström (1976), Interpolation Spaces - An Introduction (Springer, New York).
2. Daubechies, I. (1992), Ten Lectures on Wavelets (SIAM, Philadelphia).
3. De Vore R. and G. Lorentz (1993), Constructive Approximations (Springer, Berlin).
4. De Vore, L. (1985), Nonparametric Density Estimation (Wiley, New York).
5. Donoho, D.L., I.M. Johnstone, G. Kerkyacharian and D. Picard (1995), Wavelet Shrinkage: Asymptopia, J. Roy. Statist. Soc. B, 57, 2, 361-369.
6. Donoho, D.L., I.M. Johnstone, G. Kerkyacharian and D. Picard (1996), Density estimation by wavelet thresholding, Ann. Statist., to appear.
7. Johnstone, I.M., G. Kerkyacharian and D. Picard (1992), Estimation d'une densité de probabilité par méthode d'ondelettes, Comptes Rendus Acad. Sci. Paris (A) 315, 211-216.
8. Katznelson, Y. (1968), An Introduction to Harmonic Analysis (Wiley, New York).
9. Kerkyacharian, G. and D. Picard (1992a), Density estimation in Besov Spaces, Statist. Probab. Lett. 13, 15-24.
10. Kerkyacharian, G. and D. Picard (1992b), Density estimation by kernel and wavelet method: Link between kernel geometry and regularity constraints, C.R.A.S. t315, série 1, 79-84.
11. Kerkyacharian G. and D. Picard (1993), Density estimation by kernel and wavelet methods: optimality of Besov spaces, Statist. Probab. Lett. 18, 327-336.
12. Masry, E. (1994), Probability density estimation from dependent data observations using wavelets orthonormal bases, Statist. Probab. Lett. 21, 181-194
13. Meyer, Y. (1990), Ondelettes (Hermann, Paris).
14. Parzen, E. (1962), On estimation of a probability density function and mode, Ann. Math. Statist. 33, 1065-1076.
15. Peetre, J. (1975), New Thoughts on Besov Spaces, Duke Univ Math., Ser. 1.
16. Scott, D.W. (1992), Multivariate Density Estimation (Wiley, New York).
17. Silverman, B.W. (1986), Density Estimation for Statistics and Data Analysis (Chapman and Hall, London).
18. Triebel, H. (1990), Theory of Function Spaces II (Birkhäuser, Basel).
19. Tribouley, K. (1994), Practical estimation of multivariate densities using wavelet methods, Statistica Neerlandica, to appear.
20. Walter, G.G. (1990), Approximation of the Delta function by wavelets, Preprint, Umv. Wisonsin-Milwaukee.