A weighted wavelet filter and its application in function estimation
Abstract
This work concerns the application of wavelet analysis to the estimation of functions whose values are observed at unequally spaced intervals and contaminated by noise. A weighted wavelet filter based on Daubechies filter of length four is developed. Decomposition and reconstruction algorithms are created and a related function recovery algorithm has been established. Properties of the algorithms are provided. A function estimation method is derived which preserves many of the properties of Daubechies original wavelet. Furthermore, the method also applies to the situation where the variances of the uncorrelated noise vary from observation to observation and are known or estimatable.
Degree
Ph.D.
Advisors
Bock, Purdue University.
Subject Area
Statistics
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