# Reference for density estimation

I'm trying to learn about density estimation. I'm now using Silverman's book Density Estimation for Statistics and Data Analysis , but it is very hard to follow the book, without examples and exercises.

I want to learn about density estimation techniques like: kernel method, orthogonal series, maximum likelihood penalized.The Nadaraya-Watson estimator. The K-NN method.

Anyone know some reference or course about it?

• When you say "examples and exercises", are you thinking of textbook/math syle exercises? Or more demonstrations on actual data sets, for instance comparing techniques (and perhaps w/programming)? Sep 10, 2016 at 1:06
• @GeoMatt22 Both things.
– user72621
Sep 10, 2016 at 1:34
• One reason I asked is that, if you do Python and/or R at all, I imagine there are functions that do all the techniques you mention (and typically they have help & demos). You might try getting an example dataset that you like, and then "work along" as you read your text, trying out the techniques on your own data. (Unfortunately, I use Matlab mostly for code and Google/Wikipedia/Here as needed for "text", so cannot offer more specific suggestions in those areas.) Sep 10, 2016 at 1:43

There's the book

M.P. Wand and M.C. Jones (1995),
Kernel Smoothing,
Chapman & Hall/CRC Monographs on Statistics & Applied Probability

which does have exercises. I had a draft version of it as a text (for a course taught by Matt) in about 1994 and I found it quite good. The early chapters are on density estimation.

However, there's a minimum level of mathematics required to follow this kind of material, and if Silverman was too difficult you may not fare all that much better with Wand and Jones; while it has exercises it does have a similar depth.

Similarly sets of notes for this kind of material can be found online but many of them again expect that you can follow material of about that level. If you want to actually understand it, it's hard to get away from the fact that there's a certain level of mathematics needed for it.

If you can explain more about the particular difficulties it might be possible to give more specific advice.

• In general, the author writes the results in a very direct way, it's hard sometimes to follow. I think I will need to review some things in calculus and others that I've never seen like the representation of density $f$ as Fourier series.
– user72621
Sep 10, 2016 at 1:57
• "Very direct" sounds good to me, so your objection isn't clear to me. Do you mean (e.g.) too concise, without enough discussion, or something else? Sep 10, 2016 at 6:37