Wavelets and local polynomial approximation

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.