Wavelet spectral density estimation under irregular sampling
Mark E. Lehr, K. S. Lii · 2002
It has become increasingly accepted that wavelet based estimation techniques are generally better adapted to function estimates having large variations or, for want of a better term, roughness. We consider a class of nonlinear wavelet estimators for the spectral density function of a zero-mean, stationary, not necessarily Gaussian continuous-time stochastic process, which is sampled at irregularly spaced intervals. A stationary point process is used to model the sampling method. We investigate the bias as well as covariance properties of these alias-free estimators. Simulation examples are presented to illustrate the salient features of this procedure.