Newsgroup sci.stat.math 12312

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Dick Startz wrote:
> 
> Three definitive references on the distribution of the ratio of normal
> random variables are:
> 
> Fieller, E.C. (1932), 3The distribution of the index in a normal bivariate
> population,2 Biometrika  24, 428-40.
> 
> Geary, R. C. (1930), The Frequency Distribution of the Quotient of Two
> Normal Variates,2 J. of the Royal Statistical Society, Series A, 93,
> 442-446.
> 
> Hinckley, D. V. (1969), 3On the Ratio of Two Correlated Normal Random
> Variables,2 Biometrika, 56, 635-639.
> 
> I would try the last one first.
> -Dick Startz
> 
> In article , c_gordon@igkw2.agric.za wrote:
> 
> > Hi,
> >
> > Is it possible to analytically express the probability distribution for
> >
> > c = a / b
> >
> > where a and b are univariate independent normally distributed random
> variables.
> >
> snip
> >
> > Regards,
> > ---
> > Christopher Gordon                    Tel. (012) 326-4205 (w)
> > Remote Sensing                        Fax. (012) 323-1157
> > Inst. for Soil, Climate and Water     email: c_gordon@igkw2.agric.za
> > Pretoria, South Africa                       chris@bayes.agric.za
> > Standard disclaimers apply.
> --
> Richard Startz                  Internet::  startz@u.washington.edu
> Professor of Economics          voice::     206-543-8172
> University of Washington        fax::       206-685-7477
> Seattle, WA 98195-3330 USA
Also I found this treatment on the web:
http://www.seanet.com/~ksbrown/kmath308.htm
Which gives me a chance to ask a related question. Are there similar 
references/results for products of independent normally distributed 
random variables?
Thanks,
Gary Flack

Can someone point me to a paper in which the following is
derived (elegantly if possible!):
Consider a sample of size n where n is fairly small.
Draw a sample of n iid binary r.v.s having success probability theta.
Construct bootstrap sample of theta hats (proportions of success) based
on B samples with replacement.
Compute the sample empirical distribution function F of the B theta hats.
Let B go to infinity.
What function is the expected value of F(x)?
Thanks,
Frank Harrell
Division of Biostatistics and Epidemiology
U. Virginia

Hi,
    I've just put my Ph.D. proposal online (look for Ph.D. Proposal
under new links on my home page in the signature below).  My Ph.D. is
looking at using hybrid techniques (statistical and artificial
intelligence combined) with software metrics and authorship analysis
being used as case studies.
    I would be interested in any feedback on the proposals and also
with hearing from anyone with similar research interests.  Since data
isn't that easy to obtain for software metrics I wouldn't say no to
any industry collaboration either.
Cheers,
Andrew
Software Metrics Research Laboratory, University of Otago
Phone: +64 3 479 5282 Fax: +64 3 479 8311
email: agray@commerce.otago.ac.nz 
http://divcom.otago.ac.nz:800/COM/INFOSCI/SMRL/people/andrew/andrewg.htm

>I am a programmer writing a program to analyse the amplitudes of
>seismic data. I'm not a statistician and my maths is rather rusty,
>I've been ploughing through various statistics books but I haven't
>found an answer to my question, maybe the readers of this group
>could help me?
>
>The amplitudes I've been testing look fairly similar to normal or
>log-normal distributions. I've been calculating the Skewness of
>my population. I understand that a normal distribution will have
>a skewness of 0. I can calculate the expected frequencies for
>various amplitudes, but these curves naturally have a skewness of
>zero.
I am not sure what your data are.  Are they amplitudes of cos waves of
various frequencies and phases?  If so, the normal model is very poor.
Reason: amplitude is constrained to be positive.  So that is why you are
finding log-normal works OK.  And that's also why you are seeing
distributions that are skewed to the right.
I think you need to look at the Rayleigh or Rice distrib.
See Davenport & Root, and introduction to the theory of random signals and
noise.
Don't seismologists have standard approaches for this?
Bill Simpson

>From: bm373592@muenchen.org (Uenal Mutlu)
>
>... but I'm not an expert in statistics.
Yes, we know.  If you were a statistician, you would already understand
that your ideas about predicting the lottery are based on incorrect
reasoning.
Randomness and predictability are 2 opposites.  Random numbers cannot
be predicted.  If a process is thought to be random and someone shows
that the process can be predicted, then the process is proven not to
be random.  This can be done with statistics and no-one has ever shown
any Lotto to be predictable.  Therefore, the only logical conclusion is
that they are as close to random as they can get.
You are embarking on a futile endeavour, Uenal.  Stick to combinatorial
designs where you can truly making a considerable contribution.

Hi all:  I hope some of you may be willimg to give me some guidance 
on possibilities of risk ranking.
I am aware that the subject is affected by factors which can be 
listed endlessly, ranging from public perception, politics, 
commercial interests, geography, environment etc.  Many of these are 
used to raise issues which cannot easily be resolved, which inhibits 
simple ranking of risks.
On the other hand, although individuals may choose to ignore or deny 
risk evidence, or they may demand nil risk, they are nevertheless, 
for the most part, realistic about their own risks in everyday life. 
Valuable work has been done to establish factual risks in specific 
areas of interest but integrating these into a global (if crude) 
scheme could be of long term educational value.  Unfortunately, it 
would need continuous updating maintenance.
I expect work has been done to establish some logarithmic ranking, 
but I do not know where to find it, although I often wonder about the 
sources of press estimates of risk. Thanks in advance.
-- 
          Henry MacKenzie hgmac@zetnet.co.uk

William  H. Becker  wrote in article
<000020d2+000013a8@msn.com>...
> 	 Wouldn't an improved international civil calendar
>  be a great boon in many sectors; scheduling, communications, 
> better statistical comparisons, budgeting, reduced confusion, 
> fixed day-date relationships, etc. etc.?   
> 	With the upcoming start of a new year, new century, and new 
> millennium, isn't this a good time to give this issue some 
> attention ?    I sent U.S. Vice Pres. Gore info similar to that 
> covered in URL listed below and in Nov. 1993 he wrote me that the 
> idea of an improved calendar "deserves serious consideration".
>    ISN'T IT ABOUT TIME  ? ?
>  
>  	Suggest you look at ideas on Home Page for Calendar Reform at URL:
> http://ecuvax.cis.ecu.edu/~pymccart/calendar-reform.html  
>   
> billbecker@msn.com
I agree, but we can't even get Americans to move to the yy.mm.dd format from
their early American m/d/y style.  Heck, we can't even get them using the
metric system!
Gary A Howard
gary@winternet.com

H G MacKenzie wrote:
> 
> Hi all:  I hope some of you may be willimg to give me some guidance
> on possibilities of risk ranking.
> 
> I am aware that the subject is affected by factors which can be
> listed endlessly, ranging from public perception, politics,
> commercial interests, geography, environment etc.  Many of these are
> used to raise issues which cannot easily be resolved, which inhibits
> simple ranking of risks.
> 
> On the other hand, although individuals may choose to ignore or deny
> risk evidence, or they may demand nil risk, they are nevertheless,
> for the most part, realistic about their own risks in everyday life.
> Valuable work has been done to establish factual risks in specific
> areas of interest but integrating these into a global (if crude)
> scheme could be of long term educational value.  Unfortunately, it
> would need continuous updating maintenance.
> 
> I expect work has been done to establish some logarithmic ranking,
> but I do not know where to find it, although I often wonder about the
> sources of press estimates of risk. Thanks in advance.
> --
>           Henry MacKenzie hgmac@zetnet.co.uk
There is an interesting article on the editorial page of today's 1-9
wall st journal which looked at the public's skewed perception of risk.

In article <32D53060.B3D@fc.hp.com>, Karl Schultz  wrote:
>C. K. Lester wrote:
>> 
>> In response to Karl Schultz's prior post,
>> 
>> >There are no subsets.  The 168-ticket wheel will guarantee a 3-match
>> >in a 6/49 lotto.
>> >
>> >No, the first statement is correct.
>> >The "wheeled group" is the entire set of 49 numbers.
>> 
>> So, with a 6/49, buying 168 tickets using the 168-ticket wheel will guarantee
>> a 3-match...
>> 
>> So what?
>
>Because you were asking about this!!!!!
NO NO NO... sheesh almighty. I was referring to the "perceived value" of such 
a scheme... as in, "what value is buying 168 tickets for a guaranteed 
three-match?" Maybe I should have said, "Big deal."
I was not asking, "So what, why are you telling me?"
>And, right, like any method of playing lotto, playing a wheel like
>this isn't practical from a win/lose point of view.  It is just
>an interesting fact that is often useful for judging claims
>that the same result can be accomplished with fewer picks.
Well, isn't this fun? :)
Thanks!
ck

                      FINAL CALL FOR PAPERS
__________________________________________________________________
1997 IEEE International Conference on Systems, Man, and Cybernetics
Hyatt Orlando, Orlando, Florida, USA * October 12-15, 1997
Computational Cybernetics and Simulation
__________________________________________________________________
I am organizing a track at the below conference. The track will
have 2-3 sessions directed towards applied chaotic systems for
simulation, data mining, control, image processing and encryption,
and possibly other related topics connected with chaos.
Jiri Fridrich
Center for Intelligent Systems
SUNY Binghamton, NY 13902-6000
E-mail: fridrich@bingsuns.cc.binghamton.edu
Ph/Fx: 607-777-2577
___________________________________________________________________
                     Preliminary Announcement
1997 IEEE International Conference on Systems, Man, and Cybernetics
Hyatt Orlando, Orlando, Florida, USA * October 12-15, 1997
Computational Cybernetics and Simulation
Location: October 12-15, 1997 at the Hyatt Orlando in Orlando, FL.
          Room rate: $105.00 per night, single or double.
          Located in the heart of Central Florida. Easy access to
          Disney World, Sea World, Universal Studios. Golf course,
          a health club, tennis courts, swimming pools, restaurants.
Theme:    Computational Cybernetics and Simulation has been
          selected to emphasize the growing importance of compu-
          tational methods and modeling tools in the design,
          analysis, and control of complex systems. Presentations
          dealing with theoretical perspectives, new computational
          tools, new paradigms in simulation, and innovative
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Organizing Committee:
          General Chair, James M. Tien, RPI
          Technical Programs Chair, Charles J. Malmborg, RPI
          Technical Arrangements Chair, Julia Pet-Edwards, Uni-
             versity of Central Florida
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             University of Central Florida
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Call for Contributed Papers:
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DESIGNATED TOPIC AREAS:
1 Computational Cybernetics
11 Biocybernetics
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13 Pattern Recognition and Classification
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15 Fuzzy Systems
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17 Data Mining and Knowledge Discovery
18 Optimization, Heuristics, and Search Methods
2 Decision Systems
21 Cognitive Systems and Engineering
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33 Human Factors in Design
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41 Animation
42 Continuous Simulation and Applications
43 Discrete Event Dynamic Systems
44 Output Analysis
45 Simulation Languages and Software
46 Simulation Training Systems
47 Military Simulation
48 Simulation Methodology
5 System Methods and Applications
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**********************************************************************
|  Jiri FRIDRICH, Research Associate, Dept. of Systems Science and   |
|  Industrial Engineering, Center for Intelligent Systems, SUNY      |
|  Binghamton, Binghamton, NY 13902-6000, Tel.: (607) 797-4660,      |
|  Fax: (607) 777-2577, E-mail: fridrich@binghamton.edu              |
**********************************************************************
......................................................................
Remember, the less insight into a problem, the simpler it seems to be!
----------------------------------------------------------------------

Hi 
Does anyone know how to import SPlus graphs into a LATEX document using
PCTEX.
Thanks

fharrell@virginia.edu wrote:
> 
> Can someone point me to a paper in which the following is
> derived (elegantly if possible!):
> 
> Consider a sample of size n where n is fairly small.
> Draw a sample of n iid binary r.v.s having success probability theta.
> Construct bootstrap sample of theta hats (proportions of success)
> based on B samples with replacement.
> Compute the sample empirical distribution function F of the B theta
> hats. Let B go to infinity.
> 
> What function is the expected value of F(x)?
The following is not elegant, but easy.
Let P* be the estimated proportion for any bootstrap
sample of size n, and Phat be the proportion of successes in the
original sample. Let F* denote the empirical cdf of the
P* over the B bootstrap samples. 
Then, F*(x) = B^{-1} \sum_{i=1}^B I\{ P* <= x \}.
Take the expectation of this wrt to the empirical measure Ehat;
since sampling is iid,
E[F*(x) | Ehat] = E[ I\{ P* <= x \} | Ehat]
The indicator of the event inside the expectation on the RHS is
equivalent to I\{ \sum_{i=1}^n X^*_i < [nx+1] \}, where [b]
is the largest integer in b. Thus, the
expectation on the RHS is just the binomial probability
(in S-speak) pbinom([nx+1]-1,n,Phat). To get the
unconditional expectation, take the expectation
of this wrt to the sampling distribution of Phat.
i.e. sum(pbinom([n*x+1]-1,n,y/n)*pbinom(y,n,theta),y=0..n)
This is a very nasty sum of the moments of a binomial
rv which probably doesn't have a closed form. There
are some identities for sums of binomial probabilities
in terms of generalized hypergeometric functions,
incomplete beta integrals, etc... which can be found
in Johnson Kotz and & Kemp, and perhaps can be used to
simplify the above somewhat. Hope this is helpful.
-- 
***************************************************************************
Robert Strawderman, Sc.D.	Email:  strawder@umich.edu
Department of Biostatistics  	Office:	(313) 936 - 1002
University of Michigan		Fax:    (313) 763 - 2215
1420 Washington Heights		
Ann Arbor, MI 48109-2029	Web:	http://www.sph.umich.edu/~strawder/
***************************************************************************

Hi all,
   perhaps some of you may be interested in the program RANDGEN. This is
a random number generator which lets you specify an (almost) arbitrary
distribution function of the generated random numbers.
RANDGEN is freeware and can be downloaded from the following URL:
       http://qspr03.tuwien.ac.at/lo/randgen.html
Regards, Hans.
-- 
*******************************************************
**   Hans Lohninger                                  **
**   Institute of General Chemistry                  **
**   Vienna University of Technology                 **
**   Getreidemarkt 9/152                             **
**   A-1060 Vienna, Austria                          **
**   email:  hlohning@email.tuwien.ac.at             **
**   fax:    ++43-1-581-1915                         **
**   voice:  ++43-1-58801-5048                       **
**   WWW:    http://qspr03.tuwien.ac.at/lo/          **
*******************************************************

 toepfer@okstate.edu (Conrad Toepfer) in <5b0ohv$55d@news.cis.okstate.edu>
writes:
> I have generated logistic functions describing abundance of
> a threatened fish species with respect to a unit (i.e., pool) of
> habitat's position within the stream.  Two functions were
> created for two different habitat suitabilities. . .now I need to
> calculate a confidence interval for both functions together
> rather than separate intervals for each function.  Any ideas
> or any references?
Unless you know a lot about this problem I think you will have to assume
that the errors are 100% correlated. This is probably true for
publication, certainly for litigation.
Aaron C. Brown
New York, NY

C. K. Lester wrote:
> 
> In article <32D53060.B3D@fc.hp.com>, Karl Schultz  wrote:
> >C. K. Lester wrote:
> >>
> >> In response to Karl Schultz's prior post,
> >>
> >> >There are no subsets.  The 168-ticket wheel will guarantee a 3-match
> >> >in a 6/49 lotto.
> >> >
> >> >No, the first statement is correct.
> >> >The "wheeled group" is the entire set of 49 numbers.
> >>
> >> So, with a 6/49, buying 168 tickets using the 168-ticket wheel will guarantee
> >> a 3-match...
> >>
> >> So what?
> >
> >Because you were asking about this!!!!!
> 
> NO NO NO... sheesh almighty. I was referring to the "perceived value" of such
> a scheme... as in, "what value is buying 168 tickets for a guaranteed
> three-match?" Maybe I should have said, "Big deal."
The above representation of your question is much better than the
vague "So what?".
The perceived value, IMHO, is as follows.  People like to win.
If they can be sure to walk away with something, then they
might take steps to do that.  The only way to increase your
chances of winning is to play more numbers.  If you are
in the habit of playing 100+ numbers at a time and have
had a long losing streak, you might be inclined to play
the 168-ticket wheel, so that you are sure to have to make
that trip to the counter to claim a prize.  Actually, you
have a 60+% chance of getting 3 wins with 168 tickets,
but that is another story.  So, it is a psychological
thing - sure to get a win.
In the end, you are right.  Big Deal.
The wheel is just a structured way to buy more
tickets, which, in itself will increase chances.
Now, here is a real tough question for wheel experts.
If one plays 168 tickets using the wheel, they are sure
to match 3 at least once.  What does this wheel do to
one's chances to match more than 3???  There was once
a speculation that playing this wheel will reduce the
chances of matching more than 3 on one ticket.  Any
truth to this?

"Robert J. Korsan"  in <5b2voi$t49@samba.rahul.net> has a
complex sampling problem.
I have reservations about your model and your approach.
The linear model is going to cause you a lot of problems. I would be
inclined to estimate the prices at which 33% and 67% of the population
would buy your product. If the true situation is linear, this gives you
enough information to fit the line. Whether it is linear or not, these
numbers are useful information that you can estimate reliably.
Concentrating on the 0% and 100% points is not good statistical practice,
a small error in your model (say one person willing to pay $1,000 or one
person unwilling to buy at any price) makes your results useless. If you
go the 33%/67% route the sample size calculation is easy.
Also I think you will have a problem asking people about buying at a
series of prices. My guess is most people will automatically buy at the
lowest price and not buy at the highest. People do not answer surveys
according to instructions. You might try a pilot study using, say,
$0.05/$0.10/$0.20/$0.40 for one group and $1.00/$2.00/$4.00/$8.00 for
another. I would bet that the large majority of group I will say they are
unwilling to pay $0.40 and the large majority of group II will say they
are willing to pay $1.00.
I think you will have to stick with one price per person surveyed. Better
yet, I would ask the question indirectly. The trick is to get the person
to really think about the purchase decision. People are much better at
describing what they do than predicting it.
Aaron C. Brown
New York, NY

bhactuary@aol.com (BHActuary) in
<19970109161200.LAA11015@ladder01.news.aol.com> asks:
> Does anyone have insight into the maximum likelihood
> estimate and prediction error from a trading rule (or any rule)
> which has produced a profit on historical data.  Invariably,
> if you apply such a rule to future data you will get less profit
> (and sometimes even a loss)!
This is really a selection bias problem. If you select a trading rule that
did well in the past it will tend to do less well in the future. This is
true of many things. The baseball player with the best batting average by
the all-star break will probably have a lower average in the second half
of the season. The children of the tallest person in the world will
probably be shorter than he is.
However quantifying this effect requires a statistical model. The main
point of disagreement when assessing trading rules is the universe of
contemplated models. For example, consider the currently-popular "Dogs of
the Dow" approach that recommends investing in the five Dow Jones
Industrial companies with the highest dividend yields. Since 1973 this
rule has posted a performance that has about 1 chance in 1,000 of
occurring by chance.
Therefore if someone had proposed this rule in 1973 they would have strong
evidence that it works. But it was proposed in 1993 after most of the
evidence was already in. To estimate the prediction error or compute a
maximum likelihood estimate of future performance, we need to know what
universe the model was selected from. We also need a model for stock
market returns but that is much less important to this question.
If you consider any selection of five stocks per year, the prediction
error is enormous. If you consider only divisions of the Dow Jones
Industrial companies by dividend yield, the prediction error is reasonably
small.
Aaron C. Brown
New York, NY

H G MacKenzie wrote:
> 
> Hi all:  I hope some of you may be willimg to give me some guidance
> on possibilities of risk ranking.
> 
> I am aware that the subject is affected by factors which can be
> listed endlessly, ranging from public perception, politics,
> commercial interests, geography, environment etc.  Many of these are
> used to raise issues which cannot easily be resolved, which inhibits
> simple ranking of risks.
> 
> On the other hand, although individuals may choose to ignore or deny
> risk evidence, or they may demand nil risk, they are nevertheless,
> for the most part, realistic about their own risks in everyday life.
> Valuable work has been done to establish factual risks in specific
> areas of interest but integrating these into a global (if crude)
> scheme could be of long term educational value.  Unfortunately, it
> would need continuous updating maintenance.
> 
> I expect work has been done to establish some logarithmic ranking,
> but I do not know where to find it, although I often wonder about the
> sources of press estimates of risk. Thanks in advance.
> --
>           Henry MacKenzie hgmac@zetnet.co.uk
Henry:
Discover magazine devoted an issue to this subject in March, April or
May.  And it did give some references that I have found useful. 
Specifically, there was a reference to an article on Bayesian analysis
(Placing Trials in Context Using Bayesian Analysis, JAMA, March, 15,
1995 -- Vol. 273, No. 11).  However, the article, although contending it
was Bayesian, was really just a weighted Meta-analysis.  I'm guessing
that the Bayesian-ism comes from the interpretation, but YMMV.
Rodney
-- 
You can't pick your ex.
Rodney Sparapani                                        Go Blue Devils.
Duke Clinical Research Institute                        Go Packers.

Jeriad Zoghby wrote:
> 
> Help with Dirichlet Distributions:
> 
> I am looking for a text or article which discusses
> some of the properties of the multivariate ordered
> dirichlet distribution.  Any suggestions would be great.
> Thanks, JeriadThere are several papers by J.E. Mosimann that describe, model, and 
characterize the Dirichlet distributions here are some as well as some by 
other authors:
Connor and Mosimann (1969), JASA, 64:194-206
James and Mosimann (1980), Annals of Statistics 8, 183-189
Darroch and Ratcliff (1971), JASA, 66:641-643
These references and those contained within should get you started.
Bob Jernigan
Dept. of Mathematics and Statistics
American University
Washington, DC 20016
jernigan@american.edu

On risk ranking:  There are two topics which need to be separated:
absolute assessment of various risks, and subjective responses to
exposure to risk.  You can probably find an general overview in 
Scientific American, 5 or 10 years ago, say, or if you chase down
references where people argued about nuclear power plants, a bit
earlier than that.
Research shows that people are fairly poor at estimating actual
risks;  typical knowledge bases are poor.  
And subjective responses to risk are considered to exhibit 
"irrationality", at least in the way that economists use the term.
That is, there are biassing factors that one can point to, without
having a good, useful explanation for them.  Society is willing to
spend money to ameliorate or attack risks for reasons other than
"total casualties".  To name a couple:
  One BIG event is a lot worse than a lot of little events; we may
spend more time and money to reduce 1-aircrash per year, or 1-air
hijacking per year, trying to make them absolute zero, than we do
to lower 40,000 automobile fatalities.
  Risk imposed on OTHERS is far worse than risk that is self-assumed;
the rationale for control of tobacco smoking is  "second-hand smoke",
as a health hazard (rather than, as a nuisance); even though the
smoker's risk is 20 or 100 times greater than the bystander's.
Rich Ulrich, biostatistician                wpilib+@pitt.edu
http://www.pitt.edu/~wpilib/index.html   Univ. of Pittsburgh
=================question, below, about risk assessment
H G MacKenzie (hgmac@zetnet.co.uk) wrote:
: Hi all:  I hope some of you may be willimg to give me some guidance 
: on possibilities of risk ranking.
: I am aware that the subject is affected by factors which can be 
: listed endlessly, ranging from public perception, politics, 
: commercial interests, geography, environment etc.  Many of these are 
: used to raise issues which cannot easily be resolved, which inhibits 
: simple ranking of risks.
: On the other hand, although individuals may choose to ignore or deny 
: risk evidence, or they may demand nil risk, they are nevertheless, 
: for the most part, realistic about their own risks in everyday life. 
: Valuable work has been done to establish factual risks in specific 
: areas of interest but integrating these into a global (if crude) 
: scheme could be of long term educational value.  Unfortunately, it 
: would need continuous updating maintenance.
: I expect work has been done to establish some logarithmic ranking, 
: but I do not know where to find it, although I often wonder about the 
: sources of press estimates of risk. Thanks in advance.
: -- 
:           Henry MacKenzie hgmac@zetnet.co.uk

In article <19970109161200.LAA11015@ladder01.news.aol.com>,
BHActuary  wrote:
:Does anyone have insight into the maximum likelihood estimate and
:prediction error from a trading rule (or any rule) which has produced a
:profit on historical data.  Invariably, if you apply such a rule to future
:data you will get less profit (and sometimes even a loss)!
:
:Regards-
:BHActuary
Yes, see markets96_momenta.ps.Z
          %A L. Ingber
          %T Canonical momenta indicators of financial markets and
          neocortical EEG
          %B International Conference on Neural Information Processing
          (ICONIP'96)
          %I Springer
          %C New York
          %P 777-784
          %D 1996
          %O Invited paper to the 1996 International Conference on Neural
          Information Processing (ICONIP'96), Hong Kong, 24-27 September
          1996. URL http://www.ingber.com/markets96_momenta.ps.Z
          Tables of data supporting this paper are given in
          MISC.DIR/markets96_momenta_tbl.txt.Z
          MISC.DIR/markets_lag_cmi.c contains C-code for the Lagrangian
          cost function described in /markets96_momenta.ps.Z to be fit to
          data. Also included is code for the CMI derived from this
          Lagrangian.
Lester
--
 /*             RESEARCH                            ingber@ingber.com *
  *       INGBER                                 ftp://ftp.ingber.com *
  * LESTER                                     http://www.ingber.com/ *
  * Prof. Lester Ingber __ PO Box 857 __ McLean, VA 22101-0857 __ USA */

I do not know about PCTEX, but most LaTeX compilers need encapsulated 
Postscript files for figures.  Does S-plus produce these?
-- 
Gerry Middleton
Department of Geology, McMaster University
Tel: (905) 525-9140 ext 24187 FAX 522-3141

Aaron- 
Thanks for your response.
This is regressionto the mean and Stein's paradox.
How do you disinguish between chance relationships and real structural
ones.
I wonder if bootstrapping/resampling could be used for validation.
This whole discussion seems to be related to credibility theory in
actuarial circles.
If the highest ratio of fair coin flips of heads to tails has occured on
Tuesdays over the last year this means nothing.  However, you might
mistakenly use this result to reason that Tuesdays are correlated with
high ratios of heads to tails.  You can always find specious causal
relationships if your search long enough.  How do we avoid this?
Regards-
BHActuary