# [Rd] Wrong constants in sj function (sm library) (PR#2467)

**jechacon@unex.es
**
jechacon@unex.es

*Thu Jan 16 18:04:06 2003*

Full_Name: J. E. Chacón
Version: 1.6.2
OS: Windows Millenium
Submission from: (NULL) (158.49.28.155)
Dear reader,
I am studying the bandwidth selection problem for density estimation. I have
read the popular Sheather & Jones (1991) article, in which this sj function is
based, to obtain (through function hsj) the bandwidth selector which appears in
that article. The problem is that the constants appearing in Sheather & Jones
paper are wrong, and this same (wrong) constants are used in the implementation
of the method for R. The (wrong) values are a=0.92*IQR*n^(-1/7) and
b=0.912*IQR*n^(-1/9). The constants there are wrong, the correct ones are:
- For a, (16*sqrt(2)/5)^(1/7)=~1.24 and
- For b, (32*sqrt(2)/7)^(1/9)=~1.23
These corrected values appear, for instance, in the function width.SJ of MASS
library.
I hope this helps for improving this wonderful sm library.
Yours sincerely,
J.E. Chacón
P.S.: Greetings from here for Professor Azzalini, who I met at his Smoothing
Methods course in Girona (Spain), last November, 2001.