Statistical Estimation for Stationary Models with Tapered Data

In this paper, we survey some recent results on parametric and nonparametric statistical estimation about the spectrum of stationary models with tapered data, as well as a question concerning robustness of inferences carried out on a linear stationary process contaminated by a small trend. We also discuss some questions concerning tapered Toeplitz matrices and operators, central limit theorems for tapered Toeplitz-type quadratic functionals, and tapered Fejér-type singular integrals. These are the main tools for obtaining the corres ponding results, and also are of interest in themselves. The processes considered will be discrete-time and continuous-time Gaussian, linear or Lévy-driven linear processes with memory.