On practical importance of Density Estimation using Series Expansion
In lecture 20, we discussed the method of density estimation using series expansion. Here is a thought on its practical importance.
First, We quantify its level of error by comparing it to that of density estimation using window method - not with the true underlying density. So, the level rate concluded can not tell us the expected rate, which we are truly interested in.
Second, the whole idea of Series Expansion is derived as approximation to Window function. Nothing change in the basic rationale. What changes is by choosing different expansion (Fourier, Exponential, .etc.) and by choosing different m (the maximum length of the series), we gain some control on the shape of the window.In this sense, the method of series expansion can be considered as a special way to design/specify window function.
