Some uses if cumulants in wavelet analysis
- 1 January 1996
- journal article
- research article
- Published by Taylor & Francis in Journal of Nonparametric Statistics
- Vol. 6 (2-3) , 93-114
- https://doi.org/10.1080/10485259608832666
Abstract
Cumulants are useful in studying nonlinear phenomena and in developing (approximate) statistical properties of quantities computed from random process data. Wavelet analysis is a powerful tool for the approximation and estimation of curves and surfaces. This work considers both wavelets and cumulants, developing some sampling properties of linear wavelet fits to a signal in the presence of additive stationary noise via the calculus of cumulants. Of some concern is the construction of approximate confidence bounds around a fit. Some extensions to spatial processes, irregularly observed processes and long memory processes are indicated.Keywords
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