Sankhya: The Indian Journal of Statistics

2001, Volume 63, Series A, Pt. 3, pp. 394--411

SOME NEW METHODS FOR WAVELET DENSITY ESTIMATION

By

D.R.M. HERRICK, G.P.\ NASON and B.W. SILVERMAN University of Bristol, Bristol, U.K.

SUMMARY. This article proposes some non-linear, thresholded wavelet density estimators, and investigates the practical problems involved in their implementation. Our proposed thresholding method exploits the non-stationary variance structure of the wavelet coefficients. One proposed method of estimating the variances of the raw coefficients uses the scaling function coefficients. Since these are available as a by-product of the discrete wavelet transform, no extra effort is required to find them. The performance of the methodology is assessed on a real dataset from a forensic application and simulated data from a well known test function.

AMS (1991) subject classification. 62G07.

Key words and phrases. Smoothing, wavelet norms, wavelet shrinkage, gene fragment, resolution choice.

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