Wavelet spectral density estimation under irregular sampling

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.