Very many thanks to all that responded to my request for an S-plus
implementation of multivariate kernel density estimation! The responses
are summarized below.
Todd Hatfield
=====================================================
There are several places that have S-plus code for multivariate density
estimation. A very nice implementation that runs under many (all?)
S-Plus versions is based on the book "Applied Smoothing Techniques
for Data Analysis" by A.W. Bowman and A. Azzalini, and is
available via the World Wide Web at http://www.stats.gla.ac.uk/~adrian/sm or
http://www.stat.unipd.it/dip/homes/azzalini/SW/Splus/sm. Their sm.density
function does kernel density estimation up to three dimensions. The kde2d
collection in the S directory of statlib submitted by Guy Nason and
Martin Maechler does bivariate density
estimation. The collection ash in the S directory of statlib does
approximations to kernel estimation (average shifted histograms) up to 10
dimensions, based on work by David Scott. I believe that the KernSmooth
library of Matt Wand, which implements material from the book "Kernel
Smoothing" by M.P. Wand and M.C. Jones, contains code for multivariate
density estimation (it only runs under Unix, I believe). It is available
via the World Wide Web at
http://www.biostat.harvard.edu/~mwand/software.html.
You might also want to consider alternatives to kernel density estimation
that have better properties (better properties at the boundary, the
potential for higher order convergence in the interior) such as local
likelihood and penalized likelihood. Clive Loader has written a very
powerful set of routines called locfit to fit local likelihood methods
related to his book "Local Regression and Likelihood"; the code is
available at http://cm.bell-labs.com/stat/project/locfit. Chong Gu has
written a collection of Ratfor routines called RKPACK-II to do
multivariate penalized likelihood density estimation that is avilable at
http://www.stat.purdue.edu/people/chong/software.html.
Chapters 3 (univariate d.e.) and 4 (multivariate d.e.) of my book
"Smoothing Methods in Statistics" discuss these methods in more detail;
the book and the website related to the book at
http://www.stern.nyu.edu/~jsimonof/SmoothMeth/ have the details on
computing that I mention above.
Jeffrey S. Simonoff
Dept. of Statistics & Oper. Res.
Leonard N. Stern School of Business
New York University
44 West 4th Street, Rm. 8-54
New York, NY 10012-0258
USA WWW: http://www.stern.nyu.edu/~jsimonof
e-mail: jsimonoff@stern.nyu.edu
=====================================================
Try looking at the SM package by Bowman and Azzalini. Its at the Statlib
and Brian Ripley's site.
Good luck, Mark Hall
=====================================================
Loaders LOCFIT library at
http://cm.bell-labs.com/cm/ms/departments/sia/project/locfit/index.html
does multivariate density estimation via local likelihood. I think kernel
methods is a subset of local likelihood.
Regards,
Henrik Aalborg Nielsen
Department of Mathematical Modelling
Section for StatisticsFax:+45 4588 1397
Time Series GroupPhone:+45 4525 3418
Technical University of DenmarkE-mail:han@imm.dtu.dk
Building 321, 2800 Lyngby, DenmarkURL:http://www.imm.dtu.dk/~han
====================================================
The sm library associated with Bowman and Azzalini's Applied Smoothing
Techniques for Data Analysis (Oxford, 1997)
<http://www.stats.gla.ac.uk/~adrian/sm> handles kernel density estimation
with up to three variables; there is a more general function in the locfit
library associated with Loader's Local Regression and Likelihood (Springer,
1999) <http://cm.bell-labs.com/stat/project/locfit>.
I hope that this helps,
John Fox jfox@McMaster.ca
Department of Sociology McMaster University
=====================================================
My ASH (averaged shifted histogram) software is a
fast approximation to a kernel estimate. You can
find it at statlib or ftp://ftp.stat.rice.edu
in pub/scottdw/ASH.code/ash.9701.shar (and README).
This is a unix version. A partial PC version is
described in the Venables and Ripley Splus book.
Yours, David Scott
P.S. Another reference is my book "Multivariate Density
Estimation"
=================================================
Original posting:
I would appreciate it if anyone could share or point me to an S-plus
implementation of mutilvariate kernel density estimation. Many thanks.
Todd Hatfield
Westland Resource Group
1863 Oak Bay Avenue
Victoria, BC V8R 1C6
phone: (250) 592-8500
fax: (250) 592-1633
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