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From |
"Nick Cox" <n.j.cox@durham.ac.uk> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
st: RE: Silverman Test for modes |

Date |
Sun, 28 Nov 2004 16:54:26 -0000 |

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. * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**st: Re: RE: Silverman Test for modes***From:*"Stephen Pollard" <spollard777@comcast.net>

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