| It has become increasingly accepted that wavelet based estimation techniques are generally better adapted to function estimates having large variations or, for lack 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 irregular intervals. A stationary point process is used to model the sampling method. The biases as well as the covariance properties of these alias-free estimators are investigated for their theoretical aspects. Simulation examples are presented to illustrate the salient features of the properties to be expected from such an analysis. |
