Notes on Non-parametric estimation

To tie up the discussion on the topic op estimation, more specifically spectral estimation, we derive here some tighter properties related to the direct use of the Fourier Transform, as contrasted to the properties of parametric methods such as the Levinson-Schur algorithm, where parameters of a model are estimated. We shall obtain a better insight in how well the Fourier Transform on discrete stochastic time series is capable to estimate the Power Spectral Density Function (PSDF). In this section we follow the book of Stoica and Moses as mentioned, because it gives a more succinct description of the topic than can be found in the book of Porat. The discussion also gives a nice introduction to the topic of 'windows' used to preprocess the data so that the quality of the spectral estimation is enhanced to some extent.