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In this paper, we survey some recent results on statistical inference(parametric and nonparametric statistical estimation, hypotheses testing) aboutthe spectrum of stationary models with tapered data, as well as, a questionconcerning robustness of inferences, carried out on a linear stationary processcontaminated by a small trend. We also discuss some question concerning taperedToeplitz matrices and operators, central limit theorems for tapered Toeplitztype quadratic functionals, and tapered Fej\'er-type kernels and singularintegrals. These are the main tools for obtaining the corresponding results,and also are of interest in themselves. The processes considered will bediscrete-time and continuous-time Gaussian, linear or L\'evy-driven linearprocesses with memory.

Statistical inference for stationary linear models with tapered data