Jump and Sharp Cusp Detection By Wavelets (1995)
| Venue: | Recent Research on the Nitinol Alloys and Their Potential Application in Ocean Engineering,” Ocean Engineering |
| Citations: | 29 - 2 self |
BibTeX
@INPROCEEDINGS{Wang95jumpand,
author = {Yazhen Wang},
title = {Jump and Sharp Cusp Detection By Wavelets},
booktitle = {Recent Research on the Nitinol Alloys and Their Potential Application in Ocean Engineering,” Ocean Engineering},
year = {1995}
}
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Abstract
this paper we consider only jump and sharp cusp detection in one dimension. There is a great amount of statistical literature on change-points (Basseville, 1988; Basseville & Nikiforov, 1993). Wahba (1984) and Engle, Granger, Rice &Weiss (1986) were the first to estimate curves with discontinuities in derivatives, assuming the locations of the jumps are known. McDonald & Owen (1986) proposed an algorithm to compute estimates of regression functions when discontinuities are present. Yin (1988) used one-sided moving averages to find the locations of jumps in a function. Lombard (1988) described jump detection by Fourier analysis. Cline & Hart (1991) considered detecting jumps in derivatives. Muller (1992) estimated the location of a jump and its jump size by boundary kernels. Eubank & Speckman (1994) used a semiparametric approach to detect the discontinuities in derivatives of regression functions. Hall & Titterington (1992) studied edge-preserving and peak-preserving by smoothing. Grossmann (1986) and Mallat & Hwang (1992) used wavelet transformation to detect singularities and edges in computer images. The paper is organized as follows. Sections 2 and 3 introduce the white noise model and wavelet transformation, respectively. Testing hypotheses and estimation are considered in Sections 4 and 5. Section 6 discusses implementation of the detection in practice. Simulation results and an application to a real example are reported in this section. Concluding remarks are given in Section 7. Proofs are collected in the Appendix. 2. THE WHITE NOISE MODEL
