I am looking for help in choosing a suitable method for bandwidth selection in kernel density estimation.
I have six data sets with 50 to 200 observations each and aim to fit a continuous univariate pdf to this data (parametric pdf do not provide a good fit). I have stumbled across a paper which compares various packages in R for KDE such as ("density" in stats, "kernsmooth", "ks", etc.) (see paper: Deng & Wickham 2011).
My understanding so far:
I have understood that the challenge of KDE is a question of choosing an optimal bandwidth (and the Kernel). Furthermore, I understand that bandwidth selection is a problem of trading-off bias and variance as we want to avoid overfitting. Similar to other learning-techniques I would want to minimize the error in my test-set, correct? Now for densities the usual error measures would be MISE or AMISE?
From reading I have found a variety of methods which I concluded go back to following:
1. Choose bandwidth according to visual fit (which may help but may be arbitrary)
2. Using plug-ins
3. Using cross-validation
All of the above packages implement one or the other techniques for choosing an optimal bandwidth (e.g. Wand and Jones 1995, Sheather & Jones 1991, Bowman & Azzaline, etc.). Also, I suppose that the choice of an appropriate method will depend on the particular data set, etc.
I have three questions:
1) Is my understanding of the topic so far correct (third paragraph)
2) What is the basic idea of using plug-ins?
I somehow understand that these are approximations of an optimal bandwidth under some specific statistical assumptions? And this is necessary because the true distribution f is not known? Is this correct?
3) Is there any agreement about "better" methods and thus R packages (among the suggested ones) to use for bandwidth selection?
Essentially I want to avoid using outdated methods and would be glad if someone could point me to the state of the art in that direction.
Any help in form of opinions, correction or further references is highly appreciated.