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Re: Idempotence and "Replication Insensitivity" are equivalent ?

From: <pamelafluente_at_libero.it>
Date: 25 Sep 2006 13:12:48 -0700
Message-ID: <1159215168.744278.80410@m73g2000cwd.googlegroups.com>


vc ha scritto:
> Earlier, I said that the sample median regarded as an interval (50
> percentile) *is* invariant under monotone transformations.

Ok let's assume that there exists such a thing like a "sample median regarded as an interval " (it's not a correct expression but I understand that you want to mean the interval of values which minimizes the sum of absolute deviations), then you have to define what you mean by "invariance", as the definition you provided:

           m(f(X)) = f(m(X)).

does not apply to intervals. Only after you have provided such a definition of invariance, we can check if your statement is ok.

Otherwise, we are left with a sentence that does not make sense : " sample(?) median regarded as an interval (50 percentile(?) ) *is* invariant under monotone transformations ".

-P

PS
The 50 percentile has nothing to do with an interval.

We are not talking about sampling theory. We are working in the realm of descriptive stat, not inference.

Such
> treatment is customary when monotone transformations matter. When they
> do not, one can use a single value, for convenience, obtained as the
> average of two endpoints. That value of course is *not* invariant
> under monotonic transformations.
>
> > and now you are saying that "Quantiles are invariant to monotonic
> > transformations". Do you realize these are conflicting statements?
> >
> > ?????
> > I give up to understand you.
>
> Well, I cannot help with that..
>
> >
> > Do not you think that before sarcastically suggesting other people (who
> > you do not know) to read some book should make sure you have
> > understanding of what you are talking about?
>
> I
> >
> > -P
Received on Mon Sep 25 2006 - 15:12:48 CDT

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