Title :
Wavelets and local polynomial approximation
Author :
Katkovnik, Vladimir
Author_Institution :
Dept. of Stat., South Africa Univ., Pretoria
Abstract :
The principal equivalence of two nonparametric techniques the wavelet transform and the local polynomial approximation (LPA) estimates is an objective of this paper. In particular, it is shown that the LPA enables one to interpret the wavelet spectrum as a derivative of the LPA estimate with respect to the scale parameter. The equivalent continuous wavelet transform always exists for any continuous LPA. The differentiating wavelets are derived from the LPA. The asymptotic accuracy results are presented for the estimates
Keywords :
approximation theory; estimation theory; nonparametric statistics; polynomials; spectral analysis; wavelet transforms; LPA; asymptotic accuracy; continuous wavelet transform; differentiating wavelets; local polynomial approximation; nonparametric techniques; scale parameter; wavelet spectrum; wavelet transform; Africa; Continuous wavelet transforms; Convolution; Fourier transforms; Kernel; Polynomials; Regression analysis; Statistics; Wavelet analysis; Wavelet transforms;
Conference_Titel :
Time-Frequency and Time-Scale Analysis, 1996., Proceedings of the IEEE-SP International Symposium on
Conference_Location :
Paris
Print_ISBN :
0-7803-3512-0
DOI :
10.1109/TFSA.1996.547457
