Subject: Re: probability question
From: jpl@stat.ohio-state.edu (John P Lawrence)
Date: 4 Dec 1996 18:00:13 -0500
In article <584k1f$b8j@news2.charm.net>,
T. Scott Thompson wrote:
>Those of you who have been on this group for a long time will
>recognize this question as one that should be posted on sci.math.stat
>instead of sci.stat.math, but since the former no longer exists, here
>it is...
>
>Suppose that y is a random n x 1 vector distributed such that
>Pr(y'y=1)=1. Let X = {x: Pr(x'y=0)>0 }.
>
>Question: Can X have strictly positive Lebesgue measure? (If so,
>please give an example.)
No. There are at most a countable number of y's on the unit sphere that can
have positive probability. The measure of the x's associated with each
of these y's is 0. So, the measure of X is 0 (countable additivity).
>A closely related question: Suppose that x and y are independent
>random vectors such that Pr(x'x=y'y=1)=1. Must it be the case that
>Pr(x'y=0)=0?
No. Think about defining x and y to equal particular points
on the unit sphere with probability 1. You can choose them so
that x and y are orthogonal.
>This is needed to solve a real research problem, and is not homework!
>
>----------------------------------------------------------
>I don't speak for the U.S. Department of Justice.
>Any views expressed here are my own.
>----------------------------------------------------------
>T. Scott Thompson thompson@charm.net
>U.S. Dept. of Justice thompsts@usdoj.gov
>Antitrust Division (202) 307-3726
Subject: Re: multicollinearity
From: pfv2@cornell.edu (Paul Velleman)
Date: Wed, 04 Dec 1996 21:34:38 -0500
In article <32A4A3E6.634@ucdavis.edu>, jim bouldin
wrote:
> I would like to "deal with" some potentially high levels of correlation
> between the independent variables in a multiple regression so that I may
> predict the effect of changing particular ind variables on the dependent
> variable.
Your problem is clear from your first paragraph. I presume that you mean
that you want to find the effect on the dependent variable of chaning a
particular independent variable *while holding the other independent
variables constant*. If you have naturally collinear predictors, you cannot
find this effect because you probably can't change one of the collinear
variables and hold the others constant, so the question you are asking is
inappropriate for these data.
The method you mention has the effect of removing the effects of all other
predictors from one predictor of interest. What it leaves behind is not the
original predictor, but the part of that predictor not linearly predictable
from the other predictors. When you have collinearity, this part is likely
to be (and to *mean*) something quite different from the original variable.
The coefficient you estimate in a multiple regression actually refers (in a
sense) to this new variable; interpreting it in terms of the original
variable is wrong. In that sense, the method is fine. But it won't answer
the question you asked.
-- Paul Velleman
Subject: Re: Practical vs Educational
From: aacbrown@aol.com
Date: 5 Dec 1996 02:49:07 GMT
Antonio Black in <32A4EABF.423A@sfsu.edu> asks:
> Is my end user going to want me to follow non essential
> procedures, put boxes around this and red ink that?
In my experience, most jobs require you to follow lots of non-essential
procedures. Getting the job done and getting the right answer are rewarded
less than following the rules (and following the rules is rewarded less
than playing the game). This is true in statistics and elsewhere.
However, you don't have to like or accept that. If you want to do
something useful with your life you have to resolve to ignore the
foolishness. You may make less money but at least you won't waste your
time.
The issue of grading your work is entirely different. Instructors have to
guess from what you write whether you know what you're doing. If you know
something you may consider it "non-essential" to write it down; but your
instructor may not know whether or not you know. Or, as you seem to
believe, your instructor may not know what is and is not essential. The
best plan in future may be to write everything down.
Aaron C. Brown
New York, NY
Subject: Re: Pronunciation of LaTeX
From: jgarcia@kinam.ens.uabc.mx (Jose J. Garcia-Ruvalcaba)
Date: 5 Dec 1996 03:41:20 GMT
In article <56bbsb$57s@hcunews.hiroshima-cu.ac.jp>, Hideo Hirose
(hirose@cs.hiroshima-cu.ac.jp) wrote:
>In Japan, many researchers pronounce LaTeX as "latef." Is it correct? How do you
>pronounce TeX and LaTeX actually, especially in the united states?
>
>
>
In Mexico, we say something like
Lah-tej,
as the greek chi is somewhat similar, altough not equivalent,
to the spanish j.
Subject: Nonlinear Optimization with complex functions
From: Gerhard Heinzel
Date: Thu, 5 Dec 1996 11:06:36 +0100
I need to fit a complex function of a real variable to complex measured
data. To be specific, the data are electric transfer functions (measured
by a spectrum analyzer), with the frequency as independent variable and
the model is a relativly simple complex function of freeuncy typically
involving 4 to 10 unknown parameters, sometimes more.
All algorithms I found so far assume real-valued data. Of course I could
define an SSQ or chi^2 as usual and apply a general minimization
algorithm, as e.g. Nelder-Mead Simplex. But I wonder if there are
specialized, more efficient algorithms or even implementations of e.g.
Levenberg-Marquardt?
I would be grateful for any hints,
Gerhard Heinzel
=====================================================================
Gerhard Heinzel E-mail: ghh@mpq.mpg.de
Max-Planck-Institut fuer Quantenoptik
Hans-Kopfermann-Str. 1 Phone: +49(89)32905-268
D-85748 Garching -252
Germany Fax: +49(89)32905-200
=====================================================================
Subject: Statistical test based on KL-divergence available?
From: jan@atlas.informatik.uni-bonn.de (Jan Puzicha)
Date: 05 Dec 1996 10:38:44 GMT
I have been looking for statistical tests on equality of two empirical distributions. A lot of tests like Kolmogorov-Smirnoff, Cramer-von Mises and Chi-Square have been proposed and the distribution of the corresponding statistic has been analysed.
But I wonder, why I have not found any test based on the KL-divergence, which is known to be kind of a natural distance between distributions. Especially, as one has to take care of degenerate states, a natural statistic would be the following symmetrized empirical KL-statistic:
let p(i) and q(i) be two independend empirical distributions for some set of states or bins {i}, let s(i) = (p(i)+q(i))/2.
KL = sum_i [p(i) log(p(i)/s(i)) + q(i) log(q(i)/s(i))]
Questions:
1.) What is the distribution of KL under the assumption, that p and q are independent samples from the same underlying distribution.
2.) Does this yields a reliable statistical test. (some experiments done in a rather different context do indicate this).
3.) Is there any reference concerned with this topic?
Thanks a lot in advance
Jan
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