HDTenEightyP/NetNews huggingface dataset:
From: wskelly@laurel.ocs.mq.edu.au (William Skelly)
Subject: Re: Least Square Errors
Organization: Macquarie University, Australia.
Date: Wed, 9 Sep 1992 23:49:13 GMT

Anthony,

Your problem is of wide interest to many people, not
sure I can help, but I have been working on a related
problem...below is the context of this problem, something
I have been trying to sort out wrt. to my own work.  Perhaps
others could contribute...perhaps I whistling something 
other that Dixie?

Problem:  INTERPOLATION

Approach: Non-stochastic vs. Stochastic

  Non-Stochastic techniques
     polynomial fitting
     splines

  Stochastic techniques
     moving average
     kriging

Using polynomial fitting one does not preserve the original
data points --- therefore it is very useful as a global or
smoothing technique. This is also true of moving average
techniques.

Splines do preserve the original data points and spline 
fitting is a huge area (literature wise).  Generally splines
are fit locally so that changing or removing points does not
affect the entire data set.

IMHO the stochastic methods are most interesting, the class
of techniques called BLUE (best linear unbiased estimators) 
particularly those called kriging (or Gandin optimal methods
in meteorology) allow you to derive error variance estimates
so that you can where your curve is likely to be less 
reliable.


I am not sure if it is important in your case, but remember
that if you are fitting polynomials you are implicitly imposing
a certain structure on your data (true also in the case of
sin and cos functions).  

I have found the following to be extremely helpful in all
areas of interpolation, but particularly the two dimensional
cases:

Davis, J.C. 1986. Statistics and Data Analysis in Geology,
2nd Ed., John Wiley and Sons, New York.
-it also comes with software and sample data sets

Cheers,
Chris
Newsgroups: sci.math.stat
From: jsvrc@rc.rit.edu (J A Stephen Viggiano)
Subject: Re: Least Square Errors
Organization: RIT Research Corp
Date: Thu, 10 Sep 1992 15:33:07 GMT

In article <1992Sep9.150541.15735@cbfsb.cb.att.com> rizzo@cbnewsf.cb.att.com (anthony.r.rizzo) writes:

(description of polynomial regression problem greatly abstracted by current
poster)

>with which the data were collected was zeroed at 20 C.  So, the
>curve, ideally, should pass through (20,0).  

>Two options are available to me.  First, I can simply change the
>value of the constant term in my polynomial, so as to shift
>the curve up or down by the required amount.  But this will give
>me a new curve that DOES NOT minimize the squares of the errors.

Right you are. Don't do this, you don't have to.

>Second, I can re-derive the equations such that the fitted curve
>is CONSTRAINED to pass through (20,0). . . .

You can easily do this by recoding the predictors and running the regression
without an intercept term. Instead of X, X**2, X**3, X**4, create a new
predictor Q = X - 20, and run your regression on Q, Q**2, Q**3, and Q**4.

Run it with the intercept term first. Check the partial t-statistic for the
intercept term. If it's not statistically significant, it should be okay to
run the regression again, this time without the intercept. You'll get the
answer you want.

You can expand the polynomial in Q to get a polynomial in X without
too much trouble; it's only fourth degree.

> Now my questions:  

>1) Is this legitimate, or am I just whistling Dixie?  

It is completely legitimate to recode the predictors in any way you like.
You must be careful when you recode the response. You only need to recode
the predictors in this case. (What's wrong with "Dixie"? Don't you like
Dan Emmett?) Be sure to test the significance of the intercept term, though.
If it is significant, it indicates either (a) lack of fit, or (b) the
system drifted during the process, rendering the zeroing at 20 degrees
invalid. (If you made subsequent measurements at 20 degrees throughout the
process you can get an idea of how likely (b) is.)

>2) Is this a common thing to do?  If so, any references?

Sure, it's common. It's so common, I do it without even thinking too much
about it, so I don't have a reference for you. Sorry!

==Doctor FORTRAN
Newsgroups: sci.math.stat
From: dos105@rsphy2.anu.edu.au (Darren O'Shaughnessy)
Subject: Darts
Followup-To: sci.math.stat
Organization: Australian National University
Date: Sun, 13 Sep 92 07:54:56 GMT

   I'm working on a darts simulation program, and so have studied the
distribution of darts aimed at the bull by myself (an amateur player who
gets perhaps one in five or six inside the 25-ring).
   I would have expected the distribution of the darts to be approximately
normal, but it appears that the distribution is flatter on top than a
Gaussian curve with the same standard deviation, hence with relatively more
darts falling around the one s.d. area.
   At the moment, I can model this by convoluting a uniform distribution
with a normal distribution of similar variance - i.e. by assuming that the
normal errors are overlaid upon a uniformly-random bias. Can anyone think
of a more natural distribution which "looks" like this, and can be related
back to the original sources of the throwing inaccuracies (my swinging arm,
my eyes, my poor pressured mind ...)?
   Thanking you in advance of a possible discussion, depending on the
overlap of statisticians and dart-players in the population of course.

      Signed,
              Pat Rourke  (you may not have heard of me)
Newsgroups: sci.math.stat
Subject: Re: Least Square Errors
From: news@massey.ac.nz (USENET News System)
Date: Wed, 9 Sep 92 21:46:28 GMT
Organization: Massey University

In article <1992Sep9.150541.15735@cbfsb.cb.att.com>, rizzo@cbnewsf.cb.att.com (anthony.r.rizzo)
asks about the propriety of constraining a fitted quartic to pass through
a given point:
> 
This sort of thing is often done in linear regression, usually to make the
line pass through the origin. There is no objection to doing this, but it
makes the fit slightly worse elsewhere.

I have greater reservations about using a quartic. The higher degree
the polynomial, the more unstable it is. I hope you fitted it by using
orthogonal polynomials which helps with numerical stability.

I don't say it is wrong to use high degree polynomials, just be careful;
draw and examine residual plots etc (you should do this anyway).
Date: Sat, 5 Sep 1992 23:11:57 EDT
From: Vilmos Gaspar <GASPARV@wvnvm.wvnet.edu>
Newsgroups: sci.math.stat
Subject: Nonlinear forecasting

I would like to learn more on how to perform nonlinear forecasting of future
events in nonlinear dynamical systems.  Does anybody know a good book or
article to start with? Is there any software that could be used?
Thanks for your help. Please send e-mail directly to the address in the header.

Vilmos Gaspar
Dept. Chem., WVU,
Morgantown, WV 26505
Phone: 304-293-3435 ext. 22
From: wvenable@algona.stats.adelaide.edu.au (Bill Venables)
Newsgroups: sci.math.stat
Subject: Re: Testing for Normality
Date: 12 Sep 92 14:15:08 GMT
	<Bu5suB.HxM@mentor.cc.purdue.edu> <1992Sep10.124312.4391@cognos.com>
	<11SEP199206534334@amarna.gsfc.nasa.gov>
Organization: Department of Statistics, University of Adelaide
NNTP-Posting-Host: algona.stats.adelaide.edu.au
In-reply-to: packer@amarna.gsfc.nasa.gov's message of 11 Sep 92 10:53:00 GMT

>>>>> "Charles" == Charles Packer <packer@amarna.gsfc.nasa.gov> writes:

Charles> Why not use a traditional chi-square test?

I can think of two possible reasons:

1. It requires an arbitrary partition of the range into panels, *before*
   the sample comes to hand.  (In fact it really does not test normality as
   such, but rather that the grouped sample distribution agrees with a
   similarly grouped normal.)  Arbitrariness always comes at some cost.

2. In seeking to get some power against a very wide class of alternatives
   it manages only to achieve low power against any subclass, including the
   subclass of practically important alternatives.  In this sense it is not
   well focused enough.

[BTW I would be interested in a Bayesian reaction to this question.  It always
seemed to me that tests of fit could be rather an embarrassment to a Bayesian.]
--
___________________________________________________________________________
Bill Venables, Dept. of Statistics, | Email: venables@stats.adelaide.edu.au
Univ. of Adelaide, South Australia. | Tel: +61 8 228 5412  Fax: ...232 5670
Newsgroups: sci.math.stat
From: dos105@rsphy2.anu.edu.au (Darren O'Shaughnessy)
Subject: Re: Darts
Followup-To: sci.math.stat
Organization: Australian National University
Date: Tue, 15 Sep 92 05:45:22 GMT

In article <dos105-130992174724@150.203.49.43>, dos105@rsphy2.anu.edu.au
(Pat Rourke) wrote:
> 
>    I'm working on a darts simulation program, and so have studied the
> distribution of darts aimed at the bull by myself (an amateur player who
> gets perhaps one in five or six inside the 25-ring).
>    I would have expected the distribution of the darts to be approximately
> normal, but it appears that the distribution is flatter on top than a
> Gaussian curve with the same standard deviation, hence with relatively more
> darts falling around the one s.d. area.
>    At the moment, I can model this by convoluting a uniform distribution
> with a normal distribution of similar variance - i.e. by assuming that the
> normal errors are overlaid upon a uniformly-random bias. Can anyone think
> of a more natural distribution which "looks" like this, and can be related
> back to the original sources of the throwing inaccuracies (my swinging arm,
> my eyes, my poor pressured mind ...)?
>    Thanking you in advance of a possible discussion, depending on the
> overlap of statisticians and dart-players in the population of course.

    For the sake of clarity, the following:
     I am, in fact, treating the radial distance as the normally
distributed variable, with the angle uniformly randomly chosen. I then have
the option of "stretching" the distribution vertically to take account of
the fact that this is the source of more error for experienced players than
the lateral motion of the arm. However, at this stage I have assumed that
the distribution is circularly, rather than elliptically, symmetric.
   Thanking you for communication so far,

              Pat Rourke  (you may not have heard of me)
From: flim@weber.ucsd.edu (Francis Lim)
Newsgroups: sci.math.stat
Subject: Re: FORTRAN routine for fast Fourier Transform?
Date: 15 Sep 1992 23:01:10 GMT
Organization: University of California, San Diego
NNTP-Posting-Host: weber.ucsd.edu

The latest (2nd edition) version of "Numerical Recipes
in FORTRAN" now has a FFT routine I believe. However,
I'm not sure where you can obtain this on-line, or if
it is possible. You could, I suppose, purchase the book
for about $40.
-- 
==============================================================================
     FRANCIS W. LIM / email: flim@ucsd[.edu] / dept phone: (619) 534-3383
     Dept of Economics, Univ of Cal at San Diego, La Jolla, CA 92093-0508
==============================================================================
From: neil@dehn.mth.pdx.edu (John Neil)
Newsgroups: sci.math.stat
Subject: Where is |STAT being distributed?
Summary: I've lost the announcement and cannot remember the site...
Keywords: statistics, |STAT
Date: 10 Sep 92 15:16:54 GMT
Article-I.D.: dehn.neil.716138214

The subject says it.  I've lost the announcement somewhere during the Spring
cleaning on my box and cannot locate it.  If some kind soul could relay the
information to me (along with the conditions on its use, etc.) I'd appreciate
it.

--John Neil



--
John Neil, Graduate Teaching Assistant           e-mail:  neil@math.mth.pdx.edu
Mathematics Department                         NeXTMail:  neil@dehn.mth.pdx.edu
Portland State University
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
From: gdallal@pearl.tufts.edu (Jerry Dallal)
Newsgroups: sci.math.stat
Subject: Re: CART methods and software?
Summary: Where?
Date: 16 Sep 92 00:23:00 GMT
Distribution: na
Organization: Tufts University - Medford, MA
News-Software: VAX/VMS VNEWS 1.41

In article <2AB4E972.4277@news.service.uci.edu>, manderse@orion.oac.uci.edu (Mark Andersen) writes...

>I'm currently reading the CART book (by some permutation of Breiman, Freidman,
>Olshen, and Stone), and would like to know if the software they describe
>is available anywhere convenient (I know they suggest contacting one of the
>authors, but I don't recall seeing a complete address in the book; does
>anyone have it?).

Contact SYSTAT at 708/864-5670.  They were demoing the "officially sanctioned"
version (i.e., Breiman has approved it, although he's not writing code) at the
August Joint Statistical Meetings.
From: celms@vim.brl.mil (Dr. Aivars Celmins )
Newsgroups: sci.math.stat
Subject: Re: Non-linear Regression in Chemistry
Date: 10 Sep 92 17:44:20 GMT
Organization: U.S. Army Ballistic Research Laboratory, APG, MD.

In article <1992Sep3.064230.42744@kuhub.cc.ukans.edu> jeff@kuhub.cc.ukans.edu (Jeff Bangert) writes:
>A chemist has asked me to solve a problem: she has data and a model
>which is to be fit by 'least squares'.  It looks like non-linear
>regression, except that:
>
>    1. the model has two equations
>    2. both are non-linear
>    3. there are parameters common to the two equations.
>
>I would like to know:
>
>    1. is there a 'standard' method for solving this problem?
>    2. is there literature in stat or chemistry which I could read?
>

  The problem is to minimize the properly weighted sum of squares of the
  corrections ( residuals) of the *observations* (not the defects of the
  equations!) subject to the constraints given by the model equation
  system.   This leads to a constrained leaast-squares minimization.

  The minimization (least squares with model equations in form of simultaneous
  nonlinear equations) is discussed and an algorithm for the solution
  proposed in
 

   A. Celmins, Least-Squares Optimization with Implicit Model Functions, in
   "Mathematical Programming with Data Perturbations II", Anthony V. Fiacco,
   Ed., Marcel Dekker, 1983, pp. 131-152.

 
  Aivars Celmins
  celms@brl.mil
  (410)-278-6986
  
Newsgroups: sci.math.stat
From: jsvrc@rc.rit.edu (J A Stephen Viggiano)
Subject: R-Squared without Intercept
Summary: What should it be???
Keywords: regression, r-squared
Organization: RIT Research Corp
Date: Fri, 11 Sep 1992 19:57:53 GMT

In a recent post on this group, somebody described a problem whose solution, in
part, involved running a regression without an intercept term. Which leads to
today's thought.

One of the ubiquitous texts (maybe of the past -- was it Daniel & Wood?)
related an anecdote of somebody who noticed that R-squared always was
higher when no intercept term was included, so they wound up never including
the intercept term.

Does anybody have a citation for this anecdote? Does anybody have a related
story to tell? Similarly, what suggestions do you have to offer in re: R-square
from regressions without an intercept term? Thank you!
From: shimo@bcl.t.u-tokyo.ac.jp (Hidetoshi SHIMODAIRA)
Newsgroups: sci.math.stat
Subject: dist-func of mulinomial with two-way restrictions??
Date: 7 Sep 92 08:33:24 GMT
Reply-To: Hidetoshi SHIMODAIRA <shimo@bcl.t.u-tokyo.ac.jp>
Distribution: sci
Organization: Dept. of Math. Eng. and Information Physics, U of Tokyo


Dear people:

    I'd like to know the exact form of distribution function of
multinomial with marginal restrictions.  I consider the restrictions
are linear on the frequencies,  so the distribution reduces to
composite of several multinomial ones,  if the restrictions are
unoverlapped.  But I consider the following one:

    Let n_ij , i=1,...,a, j=1,...,b be two-way frequecies and p_ij be
multinomial parameters.  If there is only one restriction such as
\sum_{ij} n_ij = n, then the distribution functions becomes
P(n_ij's|n) = n! \prod_{ij} p_{ij}^{n_{ij}} / n_{ij}!.  But we
consider the following restrictions: \sum_{i} n_{ij} = m_j, \sum_{j}
n_{ij} = l_i, for i=1,...,a, j=1,...,b.  Then, what is the conditional
distribution P(n_ij's|m_j's, l_i's) ?

    I know that if i and j are independent, that is, p_{ij} = p_{i.} *
p_{.j}, then the conditional distribution can be written in explicit
from.  But I'd like to know the explicit form for the general case.

If someone knows anything about those problmes,  please let me know.

        Thank you,


 //\\\
  @ @     Hidetoshi SHIMODAIRA    <shimo@bcl.t.u-tokyo.ac.jp>
   O      Dept. of Math. Eng. & Info. Physics, Univ. of Tokyo
From: miller@cogsci.ucsd.EDU (Jeff Miller)
Newsgroups: sci.math.stat
Subject: Studentized Range Function or ASCII Table?
Date: 9 Sep 92 20:30:44 GMT
Organization: University of California, San Diego

Does anyone know where I can find a function (preferably in Pascal)
to compute percentage points of the studentized range?

How about a machine readable version of a table of critical values
(e.g., 1% and 5%)?

Thanks for any info.

Jeff Miller
jomiller@ucsd.edu
From: jerry@nutmeg.hnrc.tufts.edu (Jerry Dallal)
Newsgroups: sci.math.stat
Subject: Re: Least Square Errors
Date: 9 Sep 92 19:22:02 GMT
Organization: USDA HNRC at Tufts University

In article <1992Sep9.150541.15735@cbfsb.cb.att.com>, rizzo@cbnewsf.cb.att.com (anthony.r.rizzo) writes:

> My quandary is that the polynomial does not pass
> through the one point of which I'm dead certain, (20,0).  

Let me summarize the posting, just to be sure we're working on the same
problem.  You have some data to which you would like to fit a 4-th degree
polynomial, but the curve doesn't go where you expect it to.

There are only two possibilities (well, 3, because I'm going to split #2):

1.  The data must lie within sampling variability of the curve, or

2.  You've got model failure.  If it's model failure, there are two
     possiblities
        
     2.i.  You've specified the wrong model, i.e., it's not a 4-th degree
            polynomial, or
     2.ii. Something went wrong in the data collection process, i.e., you've
            managed to generate some invalid data.
Newsgroups: sci.math.stat
From: jsvrc@rc.rit.edu (J A Stephen Viggiano)
Subject: Re: Testing for Normality
Organization: RIT Research Corp
Date: Tue, 8 Sep 1992 20:49:13 GMT

In article <1992Sep5.064647.15570@constellation.ecn.uoknor.edu> bateman@nsslsun.nssl.uoknor.edu (Monte Bateman) writes:
>I would like to test data for normality.  The books I have
>access to talk about graphing frequencies on "probability paper".
>
>First off, I don't have any.

Available at better stationery stores. It's National form 12-083.

>Second, it seems that there should be software available 
>to do this test.

I don't know of any software, but Lillefors's test is relatively simple, and
described in many texts. Kolmogorov's test, which was the basis for Lillefors's,
requires that you _completely_ specify the distribution (including mean and
variance). Lillefors relaxed this requirement.

If you have a spreadsheet with the Gaussian CDF available as a function,
you can program it to perform this test easily. Good luck!
Newsgroups: sci.math.stat,sci.math.num-analysis
From: jja@fnbc.com (Joseph Alotta)
Subject: Stochastic Kernel Estimation?
Organization: First National Bank Of Chicago, Chicago IL, USA
Date: Thu, 10 Sep 92 14:34:48 GMT

I ran into a friend who said he interviewed with a fairly successful  
investment company.  They told him they were using stochastic kernel  
estimation to forecast prices of stocks.  ( There is a good chance they  
could be lying. )

This peaked my interest, and I would like to know if any one out there  
knows more about this methodology.  I understand using the kernel function  
to smooth a series as part of the cubic spline method.  Is there something  
more to this?

cheers,

joe.


--
==============================================================
! joe alotta                                    jja@fnbc.com !                                               
!                                             (312) 732-3439 !
!                                                            !
! "The main thing is to keep the main thing the main thing." !
! George Sweeney                                             !
==============================================================
From: rizzo@cbnewsf.cb.att.com (anthony.r.rizzo)
Subject: Least Square Errors
Organization: AT&T
Date: Wed, 9 Sep 1992 15:05:41 GMT

This is probably something that's a piece of cake for all you
stat-pros out there, but for a mere engineer the question requires
some thought and, possibly, some help.

I have experimental data, a calibration curve of sorts, for the
thermal output of a strain gauge.  I've fitted a 4th degree polynomial
to the data, by the method of least square errors, and I'm using
the polynomial to correct strain gauge readings taken at various
temperatures.  My quandary is that the polynomial does not pass
through the one point of which I'm dead certain, (20,0).  The instrument
with which the data were collected was zeroed at 20 C.  So, the
curve, ideally, should pass through (20,0).  

Two options are available to me.  First, I can simply change the
value of the constant term in my polynomial, so as to shift
the curve up or down by the required amount.  But this will give
me a new curve that DOES NOT minimize the squares of the errors.
Second, I can re-derive the equations such that the fitted curve
is CONSTRAINED to pass through (20,0).  (This would not be unlike
the application of boundary conditions by the theoretical method
in finite element problems.)  Doing so should insure that
the curve pass through (20,0), while still giving me coefficients
that minimize the square of the errors.  Now my questions:  

1) Is this legitimate, or am I just whistling Dixie?  

2) Is this a common thing to do?  If so, any references?

I thank you now, for your help later.  So does my employer, my wife, 
my children, my mortgage company, and the tax sucking municipality
that I live in.

  =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
  * Anthony R. Rizzo       |                                              *
  * The FEA Group          | There's no shortage of engineers in the USA. *
  * AT&T Bell Laboratories |                                              *
  * att.com!homxc!rizzo    | There's only a shortage of engineering.      *
  * (201) 386-2565         |                                              *
  =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
From: inlowm@cpva.saic.com
Newsgroups: sci.math.stat
Subject: two pairs
Date: 15 Sep 92 18:00:55 PST
Organization: Science Applications Int'l Corp./San Diego

The problem is that you introduced ordering by first choosing what your
first pair would be then by choosing what your second pair would be.
By counting ordered pairs you have effectively double the numerator.
Try this as your numerator:

  (13C2)*(4C2)*(4*11)

Mark Inlow
inlowm@jupiter.saic.com
From: shimo@bcl.t.u-tokyo.ac.jp (Hidetoshi SHIMODAIRA)
Newsgroups: sci.math.stat
Subject: asymptotic variance of correlation coefficient?
Date: 14 Sep 92 11:37:44 GMT
Reply-To: Hidetoshi SHIMODAIRA <shimo@bcl.t.u-tokyo.ac.jp>
Distribution: sci
Organization: Dept. of Math. Eng. and Information Physics, U of Tokyo


Dear statisticians:

    I am a graduate student and reading RAO's text book, Linear
Statistical Inference and Its Applications. I have a little question
as follows.

    In the page 362 of the book, he says: The asymptotic variance of
the product moment correlation coefficient $r$ is $(1-\rho^2)^2/n$.
He uses this result to derive the Tanh^{-1} transformation of the
correlation coefficient.

    But I cannot understand why the asymptotic variance of r is
(1-rho^2)^2/n.  If someone know the proof or any pointers, please let
me know these.

Thank you,


 //\\\
  @ @     Hidetoshi SHIMODAIRA    <shimo@bcl.t.u-tokyo.ac.jp>
   O      Dept. of Math. Eng. & Info. Physics, Univ. of Tokyo