In article <Pine.SOL.3.91.1000428162627.20489A-100000@miles>,
Greg Heath <[EMAIL PROTECTED]> wrote:
>From: Herman Rubin <[EMAIL PROTECTED]>
>Newsgroups: sci.stat.consult, sci.stat.edu, sci.stat.math
>> In article <Pine.SOL.3.91.1000428033622.20399C-100000@miles>,
>> Greg Heath <[EMAIL PROTECTED]> wrote:
>> >Date: Fri, 28 APR 2000 00:00:45 GMT
>> >From: [EMAIL PROTECTED]
...................
>> >One variable, 20 measurements per second, 26.25 seconds (526 measurements).
>> >The 1/e decorrelation time estimated from the autocorrelation function is
>> >~ 1 second. Therefore, I will get independent measurements approximately
>> >every T0 seconds (probably ~2 <= T0 <= ~ 4 sec)
>> >Could these correlated measurements have come from a Gaussian distribution?
>> >Please see my responses to the other replies.
>> Bootstrapping is totally inappropriate. However, there
>> are other simpler simulation methods of obtaining the
>> significance level, using any test statistic you wish to
>> use, assuming you are willing to use the particular value
>> of the correlation coefficient and you are using a
>> scale-invariant test. The variance will not affect your
>> test in this problem. BTW, this method is the one used
>> for obtaining significance levels for the
>> Kolmogorov-Smirnov test when parameters are estimated.
>> Construct samples according to the null hypothesis. The
>> samples should be independent; the dependence within each
>> sample should follow the model. Then use the empirical
>> distribution to determine the significance of your data set.
>Sounds good. Thank you.
>However, I'm surprised that simulation is still necessary if the
>measurements were independent instead of correlated.
>Warren Sarle (private communication) commented that decorrelating the
>series using ARIMA and testing the residuals is also a valid approach.
>However, since the variance is estimated I'd still have to use the
>simulation approach to obtain the significance level. Is that correct?
This is correct. In principle, the distribution can be
computed, but nobody has succeeded in finding a practical
way to do so; probabilities of sets in high-dimensional
spaces are not easy to obtain.
The "unusual" thing is that the distribution of something
as complicated as the Kolmogorov-Smirnov statistic, without
estimated parameters, can be computed, even asymptotically.
THIS is the lucky situation, not that it cannot be computed
in easy form with estimated parameters.
--
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
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