I am about to write my bachelor thesis about non-parametric density estimation, especially kernel density estimators and their application in classification. As I am quite new to looking for academic literature, I am having a hard time finding the most important and modern papers, or other resources, and would be glad if someone could give me a hint. Right now I am mainly working with older works (especially by Silverman and Devroye).
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3 Answers
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Kernel Smoothing by Wand & Jones was my main book reference, you can follow the literature from their bibliography. It's very well written, thin and technical just enough
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$\begingroup$ This would also be my first choice; I've read a number of books before (Silverman, for one example) and since (books by Härdle for example), but we used a pre-published draft of this book in a course Matt taught and even though it was still not quite in its final form it was quite a good book. $\endgroup$– Glen_bCommented Sep 20, 2017 at 14:42
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Adding to Aksakal, there are two more classical books that are worth recommending:
Silverman, B. W. (1986). Density estimation for statistics and data analysis. CRC press.
Scott, D. W. (2015). Multivariate density estimation: theory, practice, and visualization. John Wiley & Sons.
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$\begingroup$ Silverman has many important papers in the field $\endgroup$– AksakalCommented Sep 20, 2017 at 13:21
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Density estimation is obviously a vastly studied topic. If you care for results in density estimation with provable guarantees on sample complexity and time of computation, while having approximation up to arbitrarily low error, I strongly recommend you peruse literature from the Theoretical Computer Science community.
A starting point could be this presentation by Diakonikolas, and then, consequently this survey again by Diakonikolas. You will find folklore and more recent results on non-parametric density estimation, for discrete and continuous distributions. The references in the presentation and survey all contain pointers to a wealth of literature (with clear discussion on applications) on density estimation, studied by various communities.
I also recommend the books by Devroye-Lugosi and Devroye-Gvorfi, as well as the terse book by Tsybakov, again, if you want theoretically flavoured discussions about density estimation.
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1$\begingroup$ Another (wild) idea could be to see saddlepoint approximation from an empirical cumulant generating function as density estimation. Do not know if anythjing is written! See stats.stackexchange.com/questions/191492/… for a starting point. Could be very interesting! $\endgroup$ Commented Sep 20, 2017 at 11:48