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st: Re: RE: Silverman Test for modes


From   "Stephen Pollard" <spollard777@comcast.net>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: Re: RE: Silverman Test for modes
Date   Sun, 28 Nov 2004 11:39:16 -0800

Thanks. Will work on option 3.

I also apologize for the use of html.  I was on the road and used my web
browser to send the message which unfortunately defaulted to html.  I
usually use an email program which uses plain text as the default.

Stephen Pollard
Professor of Economics and Statistics
Cal State LA

----- Original Message ----- 
From: "Nick Cox" <n.j.cox@durham.ac.uk>
To: <statalist@hsphsun2.harvard.edu>
Sent: 11/28/2004 8:54 AM
Subject: st: RE: Silverman Test for modes


> If I understand this correctly:
>
> You may have discovered bug(s) and/or limitation(s)
> in -silvtest-. So the main options appear to be
>
> 1. Inform the authors and hope that they will
> fix it or explain what you are doing wrong
> from their point of view. Last time I looked the senior
> author was not a member of Statalist.
>
> 2. Fix it yourself.
>
> 3. Ignore -silvtest- and do this directly with
> -bootstrap- and -kdensity-.
>
> The last would seem by far the easiest. A program
> of the order of 10 lines long would appear to be
> needed to produce the mode count.
>
> I am not clear from your posting whether 50
> is also the number of observations in (one
> of) your real datasets. From my experience
> the number of modes identified by kernel
> density estimation can be very labile for
> datasets that small. This may be _precisely_
> why you are doing this.
>
> However, there is an extra generic problem
> that is very simple but also seems crucial.
> If you are counting modes as local peaks
> on the density, then minor modes that
> would not be taken seriously in practice
> are necessarily included in the count.
>
> I've found in similar problems a simple
> approach much more illuminating than this
> one. Loop over a range of kernel widths,
> and track the modes as they disappear
> and/or appear. Genuine modes can be
> expected to persist, and freak modes
> to fade away.
>
> Nick
> n.j.cox@durham.ac.uk
>
> spollard777@comcast.net (converted from original HTML)
>
> I am attempting to implement the silverman test using the procedures
> outlined by this earlier posting and from the STATA Journal:
>
> "STB-38  snp13  . Nonparametric assessment of multimodality for univariate
data
>         (help warpdenm if installed) . . . . Salgado-Ugarte, Shimizu,
Taniuchi
>         7/97    pp.27--35; STB Reprints Vol 7, pp.232--243
>         implementation of smoothed bootstrap procedure of Silverman for
>         multimodality assessment
>
> With the ado-files included you can bootstrap kde's and later to count the
> number of modes one by one interectivelly or automatically with the
silvtest.ado
> program and sending the result listing to a log file (to keep track of any
> single result)."
>
> I have successfully installed the files and can get the procedure to run.
> I am having some problems with the results.   To check the process, I
> generated a sample of 50 observations:  the first 25 observations are
> equal to the value 10; observations 26-50 are equal to the value of 100,
> so the sample has exactly 2 modes.  However, there are two interesting
> problems arising from testing for the number of modes:
>
> 1.  The number of bootstrap samples that can be generated are limited to
> the number of elements in the original sample (in this case 50).
>
> 2.  Each bootstrap sample returns only 1 mode, so that the result is
> fail to reject the null of 1 mode (even though there is clearly two modes
in my example).
>
> I have exhausted numerous possibilities of changing the different
parameters
> for this test, different examples and data sets and always get 1 mode.
> Any help would be greatly appreciated.
>
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