Statistical inference for stationary linear models with tapered data
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In this paper, we survey some recent results on statistical inference (parametric and nonparametric statistical estimation, hypotheses testing) 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 question concerning tapered Toeplitz matrices and operators, central limit theorems for tapered Toeplitz type quadratic functionals, and tapered Fejér-type kernels and singular integrals. These are the main tools for obtaining the corresponding 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.
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