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Re: st: grid point

From   Maarten buis <[email protected]>
To   [email protected]
Subject   Re: st: grid point
Date   Wed, 23 Jan 2008 09:22:10 +0000 (GMT)

--- xinzheng shi <[email protected]> wrote:
>   I would like to know how to identify the number of
> grid point in the nonparametric graph. I know the
> usual way to identify the bandwidth is
> 0.9*sd*N^(-0.2). But is there any formular to link
> bandwidth with number of grid points given that
> observation number is N. 

You don't tell us what nonparametric graph you are
talking about (there are many, e.g. -twoway fpfit-, 
-twoway mband-) but given your reference to 
bandwidth I assume you are talking about -lowess-.

There are many different ways of finding an optimal 
bandwidth, apperently your formula is one of them.
Stata however doesn't use it, it just sets the 
bandwidth by default to .8 and allows you to choose
whatever rule you feel comfortable with. I would 
warn against taking such a formula too seriously, 
such formulas are best viewed as a rules of thumb 
to be changed whenever you feel the graph looks 
funny. Bandwidth selection is still more an art 
than a science. 

The number of gridpoints is even less an issue. In 
Stata the gridpoints are set equal to the actual 
observation, which is why -twoway lowess- can be 
quite slow in large datasets. I vaguely remember 
that in the original work there was also a lot of 
discussion about the gridpoints, but that is more 
a computational efficiency problem. One of the 
nice features of it is that makes the graph rather
angular in areas where the data is sparse. To me
that functions as an automatic warning sign not
to take the graph too seriously in those areas.

Hope this helps,

Maarten L. Buis
Department of Social Research Methodology
Vrije Universiteit Amsterdam
Boelelaan 1081
1081 HV Amsterdam
The Netherlands

visiting address:
Buitenveldertselaan 3 (Metropolitan), room Z434

+31 20 5986715

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