@article {Johnstone:1997:1369-7412:319,
	author = "Johnstone, Iain M.",
	author = "Silverman, Bernard W.",
	title = "Wavelet Threshold Estimators for Data with Correlated Noise",
	journal = "Journal of the Royal Statistical Society: Series B (Statistical Methodology)",
	volume = "59",
	year = "1997",
	abstract = "Wavelet threshold estimators for data with stationary correlated noise are constructed by applying a level-dependent soft threshold to the coefficients in the wavelet transform. A variety of threshold choices is proposed, including one based on an unbiased estimate of mean-squared error. The practical performance of the method is demonstrated on examples, including data from a neurophysiological context. The theoretical properties of the estimators are investigated by comparing them with an ideal but unattainable `bench-mark', that can be considered in the wavelet context as the risk obtained by ideal spatial adaptivity, and more generally is obtained by the use of an `oracle' that provides information that is not actually available in the data. It is shown that the level-dependent threshold estimator performs well relative to the bench-mark risk, and that its minimax behaviour cannot be improved on in order of magnitude by any other estimator. The wavelet domain structure of both short- and long-range dependent noise is considered, and in both cases it is shown that the estimators have near optimal behaviour simultaneously in a wide range of function classes, adapting automatically to the regularity properties of the underlying model. The proofs of the main results are obtained by considering a more general multivariate normal decision theoretic problem.",
	pages = "319-351(33)",
	url = "http://www.ingentaconnect.com/content/bpl/rssb/1997/00000059/00000002/art00002"
	doi = "doi:10.1111/1467-9868.00071"
}