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st: Silverman Test for modes

From   [email protected]
To   [email protected], Statalist <[email protected]>
Subject   st: Silverman Test for modes
Date   Sat, 27 Nov 2004 17:48:05 +0000

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.
Stephen Pollard
Professor of Economics and Statistics
Cal State LA
PS One of the coauthors that supplied the ado files for the silverman test have also made available ado files varwiker and varwiker2 at These procedurs estimate the number of modes.  When I apply them to my bimodal sample of 50, exactly two modes are found and estimated.  Not sure why, then, the silverman test only reports back 1 mode and fails to reject the null of exactly 1 mode.


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