Quasi-Linear Wavelet Estimation

Journal of the American Statistical Association

Volumn 94, Issue 445, 1999, Pages 189-204

  Efromovich, Sam ^a  

^a UNIVERSITY OF NEW MEXICO   (United States)

Author keywords

Adaptation; Asymptotic; Besov space; Data compression; Filtering; Monotone function; Monte Carlo; Nonparametric regression; Rate optimality; Sharp optimality; Small sample

Indexed keywords

EID: 0442293816     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1080/01621459.1999.10473835     Document Type: Article

References (20)

1. Anderson, T. W. (1971), The Statistical Analysis of Time Series, New York: Wiley.
2. Birge, L., and Massart, P. (1997), “From Model Selection to Adaptive Estimation,” in Festschrift for Lucien Le Cam, ed. D. Pollard, New York: Springer-Verlag, pp. 55-88.
3. Brockwell, P., and Davis, R. A. (1991), Time Series: Theory and Methods, New York: Springer-Verlag.
4. Delyon, B., and Juditsky, A. (1996), “On Minimax Wavelet Estimators,” Journal of Applied and Computational Harmonic Analysis, 3, 215-228.
5. Devroye, L. (1987) A Course in Density Estimation, Boston, MA: Birkhauser.
6. DeVore, R. A., and Temlyakov, V. N. (1995), “Nonlinear Approximation by Trigonometric Sums,” The Journal of Fourier Analysis and Applications, 2, 29-48.
7. Donoho, D., and Johnstone, I. (1994), “Ideal Spatial Adaptation by Wavelet Shrinkage,” Biometrika, 81, 425-455.
8. Donoho, D., and Johnstone, I. (1995), “Adapting to Unknown Smoothness via Wavelet Shrink-age,” Journal of the American Statistical Association, 90, 1200-1224.
9. Donoho, D., Johnstone, I., Kerkyacharian, G., and Picard, D. (1995), “Wavelet Shrinkage: Asymptopia?” Journal of the Royal Statistical Society, Ser. B, 57, 301-369.
10. Donoho, D., Johnstone, I., Kerkyacharian, G., and Picard, D. (1996), “Density Estimation by Wavelet Thresholding,” The Annals of Statistics, 24, 508-539.
11. Efromovich, S. (1996), “Adaptive Orthogonal Series Density Estimation for Small Samples,” Computational Statistics and Data Analysis, 22, 599-617.
12. Efromovich, S. (1997), “Quasi-Linear Estimation Involving Time Series,” Computing Science and Statistics, 29, 127-131.
13. Efromovich, S., and Pinsker, M. S. (1984), “An Adaptive Algorithm of Nonparametric Filtering,” Automation and Remote Control, 11, 58-65.
14. Efromovich, S., and Pinsker, M. S. (1996), “Sharp-Optimal and Adaptive Estimation for Heteroscedastic Regression,” Statistica Sinica, 4, 925-942.
15. Hall, P., and Patil, P. (1995), “Formulae for Mean Integrated Squared Error of Nonlinear Wavelet-Based Density Estimators,” The Annals of Statistics, 23, 905-928.
16. Hârdle, W., Kerkyacharian, G., Picard, D., and Tsybakov, A. (1998), Wavelets, Approximation, and Statistical Applications, New York: Springer.
17. Juditsky, A. (1997), “Wavelet Estimators: Adapting to Unknown Smoothness,” Mathematical Methods of Statistics, 6, 1-25.
18. Kiefer, J. (1982), “Optimum Rates for Non-Parametric Density and Regression Estimates, Under Order Restrictions,” in Statistics and Probability: Essays in Honor of C. R. Rao, eds. G. Kallianpur, P. R. Krishnaian and J. K. Ghosh, Amsterdam: North-Holland, pp. 419-428.
19. Ogden, T. (1997), Essential Wavelets for Statistical Applications and Data Analysis, Basel: Birkhăuser.
20. Strang, G. (1993), “Wavelet Transforms Versus Fourier Transforms,” Bulletin (New Series) of the American Mathematical Society, 28, 288-305.