We are now going to apply our version of Kullback’s theorem based in two hypothesis to the non-parametric regression model. Assume first the following conditions:

In my most recent research, I’m working on finding “Minimax Lower Bounds” for some kind of estimators. Therefore, to learn a little more and get my ideas clear, I’ll going to start a series of posts about the topic. I pretend to make some review in the general method and introduce some bounds depending on …

The last post I forget to say that we use Mikownski classes of densities because the MISE is a risk corresponding to the $latex {\mathbb L^2({\mathbb R})}&fg=000000$ norm. Thus, it is natural to assume that $latex {p}&fg=000000$ is smooth with respect to this norm. Another way to describe smoothness in $latex {\mathbb L^{2}({\mathbb R})}&fg=000000$ are …