In article <[EMAIL PROTECTED]>, Glen Barnett <[EMAIL PROTECTED]> wrote: >Herman Rubin wrote:
>> In article <a5daqb$72k$[EMAIL PROTECTED]>, >> Chia C Chong <[EMAIL PROTECTED]> wrote: >> >Hi! >> >Does anyone come across some Matlab code to estimate the parameters for the >> >Cauchy PDF?? Or some other sources about the method to estimate their >> >parameters?? >> What is so difficult about maximum likelihood? Start with a >> reasonable estimator, and use Newton's method. >There are difficulties with Newton's method (and many other >hill-climbing >techniques) because the cauchy likelihood function is generally >multimodal. >You can end up somewhere other than the MLE unless you use a somewhat >more >sophisticated starting point than "a reasonable estimator". There are >good >estimators that can start you off very close to the true maximum, but >it's >a long time since I've seen that literature, so I can't name names right >now. The Cauchy likelihood function is frequently multimodal; for large samples for the center with known spread, the probability of unimodal is about .13. However, for reasonable sample sizes, the other modes will be "way out", and will be small. For squared error loss, the best translation invariant estimator (the Pitman estimator) can be computed by a closed formula, but I would be concerned about the numerical error if it is not done using considerably higher precision. It can also be done by numerical integration, which is not that difficult. However, I believe that the MLE will be rather good for moderate samples. The local MLE starting with quantile estimates should work quite well. Also, if one knows it is Cauchy, there are estimators using a few quantiles which are close to efficient. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399 [EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558 ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at http://jse.stat.ncsu.edu/ =================================================================
