Consistency of risk estimation with thresholding of wavelet coefficients
Tóm tắt
The paper considers the thresholding of coefficients in the expansion of a signal function on a wavelet basis. The approximate relations between theoretical risk and its estimate through soft and hard thresholdings with the universal threshold choice are given.
Tài liệu tham khảo
S. Mallat, A Wavelet Tour of Signal Processing (Academic, San Diego, 1999).
C. Chui, An Introduction to Wavelets (Academic, Boston, 1992).
C. Stein, “Estimation of the Mean of a Multivariate Normal Distribution,” Ann. Statist 9, 1135–1151 (1981).
D. Donoho and I. Johnstone, “Adapting to Unknown Smoothness Via Wavelet Shrinkage,” J. Amer. Stat. Assoc. 90, 1200–1224 (1995).
D. Donoho and I. Johnstone, “Ideal Spatial Adaptation Via Wavelet Shrinkage,” Biometrika 81, 425–455 (1994).
H. David and H. Nagaraja, Order Statistics (Wiley, New Jersey, 2003).
M. Kendall and A. Stuart, The Advanced Theory of Statistica, Vol. 1 Distribution Theory (Charles Griffin & Company Limited, London, 1961).
P. Bickel, “Some Contributions To the Theory of Order Statistics”, in Proc. 5th Berkeley Symp. on Math. Statist. and Prob, Berkeley, 1967 (Univ. of Calif. Press, Berkeley, 1967), Vol. 1, pp. 575–591.