[R] density estimation in two dimensions

[Prof Brian D Ripley]

On Mon, 19 Jun 2000, Mauricio O Calvao wrote:

> Hello,
> 
> I am a newbie to R and the subject of density estimation in two
> dimensions or more.
> 
> I would like to have some advice concerning a comparison between the R
> packages
> for density estimation in bivariate or higher order problems; I mean
> explicitly
> the packages:
> 
> 1) ash
> 2) KernSmooth
> 3) locfit
> 4) sm.

There's also function kde2d in package MASS.

ash is old, and ash2 is quite limited, in particular to product kernels.
bkde2D in KernSmooth and kde2d in MASS are essentially the same,
and sm.density in sm is again the same with a bit more interface glue.
locfit is different (it's not kernel density fitting per se) but I find it
hard to use due to lack of documentation (even with a copy of Loader's
book to hand -- in part because every version seems slightly different).

> My specific problem now is having a set of numerical pairs (x_i, y_i),
> arising from
> a computer simulation, and wanting to define a continuous function to
> play the
> role of a probability density in the space of (x, y) variables...
> 
> If possible I would also like to have some words about the corresponding
> books:
> 
> 1) Scott, "Multivariate density estimation"
> 2) Wand and Jones, "Kernel smoothing"
> 3) Loader, "Local regression and likelihood"
> 4) Bowman and Azzalini, "Applied smoothing techniques"

They do not really do much on this topic, not even Scott's.  For a
beginner, Bowman and Azzalini was the top choice on the smoothing
email list, and gets my vote too.

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272860 (secr)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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