Density estimation is the study of optimal methods for estimating probability densities. It comes in two flavors: parametric and nonparametric. Parametric estimation is solved in the usual point estimation way. Nonparametric density estimation is much less straightforward. A classic example of a nonparametric density estimate is the histogram, which like all density estimates is both a useful graphical summary of data and an important object for statistical analysis.
Multivariate Density Estimation: Theory, Practice, and Visualization
David W. Scott
- In-text exercises
- Color Versions of Figures and Datasets
We like this book's didactic approach to nonparametric density estimation. It starts with the histogram and develops it into kernel density estimation and multivariate density estimation. The text is very readable, and there are a lot of bonus topics, such as regression and mode hunting. The downside of this book is that there are no solutions to the exercises and no code examples. It's fairly easy to find code in many languages that does basic nonparametric density estimation though.
Density Estimation for Statistics and Data Analysis
This monograph is the classic text on density estimation. There are no exercises, and it's fairly short. However, if you do a lot of density estimation you'll benefit from this master's perspective.