HDTenEightyP/NetNews huggingface dataset:
From: eemn@cc.newcastle.edu.au (Brett Ninness)
Subject: SLLN and CLT for dble. index RV ?
Organization: University of Newcastle, AUSTRALIA
Date: Tue, 14 Apr 1992 22:14:01 GMT

I've proved strong convergence of an estimator arising in engineering
problems using the following SLLN:

{X_k} independent, E[X_k] = 0, 

lim_{N\rightarrow\infty}\sum_{k=1}^N\frac{E[X_k^2]}{k^2} < \infty

gives

\frac{1}{N}\sum_{k=1}^M X_k \rightarrow 0 with probability one.

The only twist is that my sequence {X_k} is double indexed: {X_{k,N}}.
That is, the variances of the X_j in

X_1,X_2, ....... X_k

are different to the variances of the X_j in 

X_1,X_2,.........X_k,X_{k+1}.

To put it another way, the variance of a particular X_k depends on how
may terms I have in the sequence, hence the double indexing.  All the terms
are zero mean and independent no matter how long the sequence.

The question is, does this affect my use of the aforementioned SLLN ?.

I also have the same problem with my proof of asymptotic Normality using
Lindberg's Theorem with Lyapunov's condition.

If someone could point me towards some references on SLLN and CLT for 
doubly indexed random variables I would be very grateful.

Brett Ninness
Dept. Elec. Eng.
University of Newcastle.
AUSTRALIA

eemn@cc.newcastle.edu.au
From: lavinus@csgrad.cs.vt.edu (Joseph Lavinus)
Newsgroups: sci.math.stat
Subject: Seeding random number generators
Date: 15 Apr 92 21:07:26 GMT
Organization: VPI&SU Computer Science Department, Blacksburg, VA

Hello!

Is there a statistically acceptable way to seed a random number generator
in a computer program?  I'm using the following RNG (the multiplicative
congruential "minimal standard" published in Communications of the ACM
a while back):

   Z(i) = 7**5 Z(i-1) mod (2**31 - 1)
   Z(0) = seed

I've been using the program's process id as a seed, but
  (a) I'm not at all sure that's a good idea, and
  (b) Suddenly I need several RNGs simultaneously.

So, the question is, is there a statistically "good" way to seed a number
(say 10, for concreteness' sake) of RNGs, such that they do not act the same
each time the program is run, and such that each stream is statistically
independent of the others, without requiring any intervention from the user?

Also, I'm certainly open to arguments about why I should use a RNG other
than the one described above...

Many thanks in advance,

Joe
-- 
______________________________________________________________________________
 Joseph W. Lavinus, Virginia Tech   /o)\    email: lavinus@cstheory.cs.vt.edu
 1001 University City Blvd., #F-9   \(o/  Blacksburg, VA 24060 / 703-953-2678
 "Let me play with it first and I'll tell you what it is later" - Miles Davis
From: dmatthews@uap.umd.edu
Newsgroups: sci.math.stat
Subject: Re: Smoothing
Date: 17 Apr 92 12:55:59 GMT
Reply-To: dmatthews@uap.umd.edu
Organization: IPST, U. of Maryland, College Park

In article <1992Apr16.221121.20217@m.cs.uiuc.edu>, marick@m.cs.uiuc.edu (Brian Marick) writes:
>
>I am looking for references that might help me with the following
>problem.  (In short, I need references to data smoothing techniques.)
>
...
>A completely different approach would be fine, too.  I chose this
>because it's visual and intuitive.

Why not FFT the data, MULTIPLY it by a suitable transfer function (lowpass
filter) which you draw yourself, and inverse FFT the multiplied data?  You
can get the impulse response by inverse FFTing the transfer function.  Avoid
steep sides and sharp corners in your lowpass filter.  This way you know
exactly what you're doing to the data.  The transfer function must multiply
both the real and imaginary parts of the FFT.  Email me with further questions
.  Easy -- use available FFT package, write the filter in a few lines.

Dr. David L. Matthews, IPST, Univ. of Maryland, College Park MD 20742-2431 
Telephone  (301)405-4830	Internet   dmatthews@uap.umd.edu
FAX 	   (301)314-9363	NSI/SPAN   UMDUAP::DMATTHEWS
Organization: Brigham Young University
Date: Thursday, 16 Apr 1992 21:31:12 MDT
From: Stewart J Mayhew <ECOSJMG@BYUVM.BITNET>
Newsgroups: sci.math.stat
Subject: What is Jensen's Theorem?

Can somebody please e-mail me a short explanation of Jensen's inequality
    and/or give me a citation where I can find a statement and proof
    of same?  Thank you very much.  Stewart Mayhew     ecosjmg@byuvm.byu.edu
From: robbie@bacchus.harvard.edu (Rob Strawderman)
Newsgroups: sci.math.stat
Subject: Re: What is Jensen's Theorem?
Date: 17 Apr 92 16:27:19 GMT
Organization: Harvard School of Public Health, SDAC

Jensens Inequality
------------------

If X is an L-1 random variable and g(.) is a convex function, then

E( g(X) )  >=  g( E(X) )


See Chow and Teicher "Probability Theory" Section 4.3 (this may give more
explanation than you are interested in).  You might also try
"A First Course in Probability" by Sheldon Ross, or
"Approximation Theorems of Mathematical Statistics" by Robert Serfling.

Rob Strawderman
Dept. of Biostatistics
Harvard University


Newsgroups: sci.math.stat
From: marick@m.cs.uiuc.edu (Brian Marick)
Subject: Smoothing
Organization: University of Illinois, Dept. of Comp. Sci., Urbana, IL
Date: Thu, 16 Apr 1992 22:11:21 GMT


I am looking for references that might help me with the following
problem.  (In short, I need references to data smoothing techniques.)

For the UNIX kernel, I can measure the effects of two input
distributions, but I cannot capture them directly.  To simplify, let's
say that the effect is the number of times each routine in the kernel
(total around 5000) is called.

I can linearize this data by numbering routines in the order they're
found in the source.  Related routines will be close to each other (to
a *very* rough approximation -- but probably good enough for now).
I can use the routine number as the X axis, entry count as the Y axis.
This will be a wild point blur:  calls to adjacent routines may differ by
a factor of more than a million.

I need to compare two point blurs to see (very roughly) whether
they're similar or quite different.  What I am thinking of doing is
smoothing them to a curve and matching the curves by eye.  I know
about Tukey/EDA style smoothing.  I know a little bit about LOWESS.  I
don't know enough to say whether or when each is appropriate.  (That
is, I need to read papers or books that say more than just "this is a
technique"; I also need "... and here's where it's most useful, and
here are the dangers".)  Where can I learn what I need?

Also, I need programs to support whatever techniques I use.  I have
ready access to SYSTAT and STATA.

A completely different approach would be fine, too.  I chose this
because it's visual and intuitive.

Thanks.

Brian Marick, marick@cs.uiuc.edu, uiucdcs!marick
Testing Foundations:  Consulting, Training, Tools.
From: charlie@umnstat.stat.umn.edu (Charles Geyer)
Newsgroups: sci.math.stat
Subject: Re: Seeding random number generators
Date: 16 Apr 92 19:18:51 GMT
Article-I.D.: news2.1992Apr16.191851.7527
Organization: School of Statistics, University of Minnesota

In article <2532@creatures.cs.vt.edu> lavinus@csgrad.cs.vt.edu (Joseph Lavinus)
writes:

> Is there a statistically acceptable way to seed a random number generator
> in a computer program?

In article <1992Apr16.144525.25017@galileo.cc.rochester.edu>
em@merlin.cvs.rochester.edu (Ethan Montag) replies:

> Someone once told me to generate one more random number at the end
> of your application and save it.  Then use it as the seed next time
> you run.  That way you have a new random seed each time you run.

Arrgh!  If you're going to save something between runs, save the *seed*
so you get one continuous run of the generator.  This is the Right Thing.
Anything else is a lazy hack.

-- 
Charles Geyer
School of Statistics
University of Minnesota
charlie@umnstat.stat.umn.edu
From: cuddon@eng2.eng.monash.edu.au (Andrew Cuddon, Civil Postg.)
Newsgroups: sci.math.stat
Subject: ANOVAs for Linear Regression - Q1
Date: 15 Apr 92 05:02:24 GMT
Organization: Faculty of Engineering, Monash University

Regards to all,
I would appreciate some feedback on a lack of understanding.

I have a situation where I would like to determine if a constant term 
is neccessary for my simple linear regression model. I have become rather
confused over how an analysis of variance table is calculated when a 
CONSTANT term is not included in a linear regression.

My model produces R2 value of 0.7 with the constant term being significantly 
different from zero at the 1% level. In the interests of simplifying the model 
I re-ran the regression without the constant term and noted an increase in R2 
to 0.9.

This was fine but I also noted that the REGRESSION SUM OF SQUARES in 
the ANOVA table increased from 14.6 up to 375.4. This was because the TOTAL 
SUM OF SQUARES increased from 20.4 up to 381.5. If the two models are from the 
same data set, how can the TSS be different in each case? I believe this may 
be something to do with correcting for the mean but I don't really understand 
what is going on here.

Thanks in advance,
=============================
Andrew Cuddon
CUDDON@ENG2.ENG.MONASH.EDU.AU
=============================
Newsgroups: sci.math.stat
From: davidb@psych.toronto.edu (David Brodbeck)
Subject: Help, I need book advice about SAS
Organization: Dept. of Psychology, University of Toronto
Date: Wed, 15 Apr 1992 14:55:08 GMT


Hi, I'll be teaching a course on ANOVA and Regression with SAS in the fall.  I
need some recomendations from people on a good text (need to know the 
publishers as well).  Any help would be appreciated.  Please respond by
Email.  I'll summarize to this group is there's interest.
Dave Brodbeck
-- 
                          Dave Brodbeck - U of T Psych
                     The chickadees are not what they seem
                            davidb@psych.toronto.edu
From: oliver@athena.mit.edu (James D. Oliver III)
Newsgroups: sci.math.stat
Subject: IQRs and hypothesis testing
Date: 15 Apr 92 09:43:24 GMT
Organization: Massachusetts Institute of Technology

I was using a packaged statistical program to do some simple means testing,
and notice that in several cases the program didn't do a straightforward
t-test, but instead "computed the standard error of the difference of means
assuming IQR(pop.1)/IQR(pop.2)= X".

I found out what IQR is (interquartine(sp?) range) and have a general
understanding of what it is, but can find no references on the specifics of
this particular adjustment and/or the justification for using it.

Can anyone point me to some basic, low-level references on this?  Also, if
there is a similar procedure in conjunction with one-way analysis of
variance?
--
____________________________
	Jim Oliver  
	oliver@athena.mit.edu /	joliver@hstbme.mit.edu
	oliver%mitwccf.BITNET@MITVMA.MIT.EDU
Organization: TECHNION - Israel Institute of Technology.
Date: Sunday, 5 Apr 1992 18:08:42 IST
From: <IERYT01@TECHNION.BITNET>
Newsgroups: sci.math.stat
Subject: Suggestions for Analytic Chem Stat Package

I'm looking for a PC stat package that contains analyses that are of
interest to analytic chemsists.  Examples of such analyses:
calibration analysis
repeatability and reproducibility
limits of detection and criterion of detection
screening for outliers within groups of replicates (Dixon's test)

Thanks in advance for any suggestions.

Yossi Tal
Faculty of Industrial Engineering and Management
Technion, Israel Institute of Technology
Newsgroups: sci.math.stat
From: Andrew.Robinson@anu.edu.au
Subject: Re: sampling-simulation
Reply-To: Andrew.Robinson@anu.edu.au
Organization: Australian National University
Date: Wed, 15 Apr 92 05:28:22 GMT

In article <1992Apr14.201524.26090@unixg.ubc.ca> umsk@unixg.ubc.ca (HanJoo
Ecom) writes:

[munch]

>If I calculate a mean and variance, and confidence interval for the
>population value based on 2000 replications, would there be substantial
>differeces among the 7 options?  If so, how one could justify the 
>use of a particular method in a simulation study?
>
>  Many thanks for your time in advance.

A and B should not differ. (i.e. 1 and 5, 2 and 6, 3 and 7 are to all intents
identical, and 4 has no corresponding infinite population case)

If you use the correct formulae, the results otherwise should not differ
siginificantly also.  I can't recall whether there is a difference between
sampling with replacement and without replacement in terms of efficiency, but
with those population sizes I'd be surprised if there was.
  
The method should be dictated by the nature of the process which is being
simulated.  If you have a theoretically infinite population as your target,
then use that for your simulation.  If you don't, and you know the pop. size,
then use that instead.  Or approximate it if you don't know it.  The same
applies to which sampling technique you choose.

regardless,
&rue

Andrew.Robinson@anu.edu.au   <= forestry statistician 
(if it moves, count it; if it doesn't move then CHOP IT DOWN and count it.)
My employers don't care what I say, in fact I don't even think they know I
exist.
From: mwande@qal.qal.berkeley.edu (Mike Anderson)
Newsgroups: sci.math.stat
Subject: re: SPSS export files
Date: 17 Apr 1992 05:33:57 GMT
Organization: University of California, Berkeley
Distribution: world
NNTP-Posting-Host: qal.qal.berkeley.edu


Oh, BTW, the export was done with SPSSx 2.1 for PRIME, and
I am trying to import it with SPSSx 3.1 for VM/CMS, if that
makes any difference. I also pinpointed the point in the
export file where the job chokes, and there is nothing funny
there. I strongly suspect, then, that this is some sort of
compatibility problem. Possible?
Thanks, Mike

-- 
-----------------------------------------------------------------------------
Mike Anderson    Dept. of Demography   UC Berkeley   mwande@QAL.Berkeley.EDU
"It's the little touches that make a future solid enough to be destroyed."
                                                - William S. Burroughs
From: mwande@qal.qal.berkeley.edu (Mike Anderson)
Newsgroups: sci.math.stat
Subject: SPSS export files
Date: 17 Apr 92 04:15:26 GMT
Article-I.D.: agate.sljcuINNbgh
Organization: University of California, Berkeley
NNTP-Posting-Host: qal.qal.berkeley.edu


This is more of a computer question that a stats question, but I don't
know where else to post it (do you?)
My problem is that some time ago, I exported an SPSSx system file
off of a PRIME system and put it onto a floppy disk. I have recently
found a need for the data set, so I uploaded it to my present account
(VMS) and tried to import it. I get a message that a premature end of
file was encountered. When I look at the file though, everything
seems to be there, and the end of the file is marked by a string
of ZZZZ's like it should be. I sthere a problem in compatibility?
I've also tried to convert it to a SAS file, and something similar
happend: it gets part way through the job and quits. The listing has
some of the variable names and characteristics, but no observations.
Has anyone else had similar problems, answers?
Thanks in advance, Mike Anderson

-- 
-----------------------------------------------------------------------------
Mike Anderson    Dept. of Demography   UC Berkeley   mwande@QAL.Berkeley.EDU
"It's the little touches that make a future solid enough to be destroyed."
                                                - William S. Burroughs
Newsgroups: sci.math.stat
Subject: "Half or plus".
From: wft@math.canterbury.ac.nz (Bill Taylor)
Date: 10 Apr 92 18:08:54 +1200
Distribution: world
Organization: Department of Mathematics, University of Canterbury

This one has bothered me for a long time.


"HALF-OR-PLUS" is a simple discrete-time stochastic process. 
 ~~~~~~~~~~~~
Start with value 1; and at each time step, either halve or add one to the current
value, with probability 1/2 each, independently of what's happened before.


Formally....    Y   = 1
                 0

                        /   Y  + 1  .....   if  X = 0
                       /     n                   n
              Y     = <
               (n+1)   \    Y  / 2  .....   if  X = 1
                        \    n                   n

where { X  } is a Bernoulli sequence with parameter 1/2 .
         n
-----

This is a Markov process, and, as always, one is interested in the long-term
behaviour of it.  

Intuitively, as the value is bounded below by zero, but downward moves are 
more "damaging" than upward ones (at least to large values), one would expect
that it would "settle down" to a reasonable statistcal behaviour. That is,
one might hope that the probability distribution of Y(n) would tend to
some fixed distribution on R+ , seemingly with most of its weight near the
left end.

Indeed, if the transition rule were more diffuse, that's what we would get,
fairly straightforwardly.  But the trouble here is, the state space for this
process, i.e. the set of values any of the Y(n) might take, is a discrete
set, though an unusual one. Specifically, the state space is the set of
positive dyadic fractions
                           S = { m/2^n : for integer m>0, n>=0 } .

So the probability distribution for each Y(n) is discrete, supported by 
a finite subset of S .

And it seems to be exceedingly difficult to calculate what the limiting
(continuous) probability distribution is. It's not even 100% clear that 
there WILL be a limiting distribution, though I feel sure there must be !

It seems reasonably easy to calculate (numerically), coarse approximations to 
the limiting distribution; i.e. the limiting discrete distribution on the set 
of disjoint intervals of unit width; or of half-unit width; and so on. 
But it's frustrating trying to extend the results to a continuous distribution.


Anyone who can provide help on this problem will earn my gratitude.

---
Bill Taylor.                  wft@math.canterbury.ac.nz 

Xref: sparky sci.math.stat:1002 sci.math:6055
From: umsk@unixg.ubc.ca (HanJoo Ecom)
Newsgroups: sci.math.stat,sci.math
Subject: sampling-simulation
Date: 14 Apr 92 20:15:24 GMT
Organization: University of British Columbia, Vancouver, B.C., Canada

Dear Readers;

I would greatly appreciate your feedback/comments/remarks etc
as well as any reference sources on the following issue.

I am recently involved in a simulation study to investigate the
degree of sampling variability and possible bias of estimates.
I am using a multivariate-normal random number generator to obtain
sample data with a specified population covariance matrix as an input.

I am considering to choose one of the following sampling methods to
generate a set of sample data (say 2000 samples, each having n=100)
and subsequently calculate sample statistics from each sample.

A) assume an infinite population size and;
  1) generate a sample size of 100 and repeat this 2000 times, or
  2) generate a sample size of say 200000 and randomly select
     a subsample of 100 for 2000 times without replacement, or
  3) the same as 2), but with replacement.

B) assume a finite population size and ;
  4) generate a population (1000000 values) and select a random
     sample of size 100, 2000 times without replacement, or
  5) the same as 4), but with replacement, or
  6) generate a population (say 200000 values) and select a random
     sample of size 100, 2000 time without replacement (thus,
     every value in the population would be selected exactly once), or
  7) the same as 6), but with replacement.

If I calculate a mean and variance, and confidence interval for the
population value based on 2000 replications, would there be substantial
differeces among the 7 options?  If so, how one could justify the 
use of a particular method in a simulation study?

  Many thanks for your time in advance.

Hanjoo Eom (e-mail: umsk@unixg.ubc.ca)
Department of Education
Univ. of British Columbia
Vanc. B.C., Canada.
From: drumhell@n5160a.nrl.navy.mil (David Drumheller)
Newsgroups: sci.math.stat
Subject: Continued fractions and special functions.
Keywords: continued fractions, special functions
Date: 6 Apr 92 12:56:09 GMT


    During the course of my research in the application of order
statistics to detection theory, I found it necessary to compute
the incomplete gamma function.  I used a routine from Numerical
Recipes in C (by Press et al) which is based on a continued fraction
expansion.  None the of references in the book contain a derivation
of this expansion.
    
    Question: does anybody know of a reference that gives a
explanation/derivation of the continued fraction expansion of the
incomplete gamma function or any other special functions?

    More generally, does anybody know of a good reference on
continued fractions?

    Please e-mail responses to me directly.  Thank you!
    
Dave Drumheller
Naval Research Laboratory
Acoustics Division, Code 5160
Washington, D.C.  20375
USA
(202) 767-3524
e-mail address: drumhell@n5160a.nrl.navy.mil
From: vinson@shiva.seas.upenn.edu (Jack Vinson)
Newsgroups: sci.math.stat
Subject: simple hypothesis testing
Date: 7 Apr 92 18:30:36 GMT
Followup-To: me
Organization: The University of Pennsylvania


Is it legal to use the usual student's t test to test whether a single
sample is taken from a larger sample?  i.e.  I have an average of previous
samples and their variance, can I determine if a new sample is from the
same distribution with some confidence the same way I would check if the
average were equal to some expected value?

It doesn't seem quite right to check the same way.  The usual test asks
about the difference between the sampled average and the expected value.
My test will ask about the difference between the sampled average and a
sampled value.

Jack Vinson			The Purple Puddle Eater
vinson@shiva.seas.upenn.edu
vinson@unagi.cis.upenn.edu
Newsgroups: sci.math.stat
From: jil@linus.mitre.org (Jon Leivent)
Subject: help needed with Markov flipflop
Organization: Research Computer Facility, MITRE Corporation, Bedford, MA
Distribution: sci.math, sci.math.stat
Date: Thu, 2 Apr 1992 22:02:45 GMT


I need some help finding an analytic solution for a seemingly simple
Markov chain problem.  The chain (in discrete time) consists of two
states, A and B, arranged as a flip-flop.  The one-step probabilities
are: A to A is q, A to B is 1-q, B to B is r, B to A is 1-r.  Here's a
diagram of the chain:

    q          r
   +-+        +-+
   | |        | |
   | V        | V
  +---+ 1-q  +---+
  |   +----->|   |
  | A |      | B |
  |   |<-----|   |
  +---+  1-r +---+


The initial condition is that we spend the first time step in state A.
I'm trying to find the probability distribution function P(C,S), which
gives the probability that after S steps, the count of the number of
steps spent in state A is C (C is thus the "total sojourn time" in
state A).

The initial condition, expressed in terms of P, is P(1,1)=1.
Obviously, there's also a normalizing condition, that the sum over all
C of P(C,S) is 1 for any S.

I've tried several different techniques.  One way, I end up with a
linear partial difference equation for P that has a very complex
non-constant coefficient that prevents me from solving it.  Another
way, I end up with a system of 2 linear partial difference equations
that I can solve, but I can't determine the correct linear combination
of the solutions to fit the initial values.

One thing I can find is the probability of being in state A at step S:

                  (S-1)
       (q-1)(q+r-1)     + r-1
Z(S) = ----------------------
                 q+r-2


I would appreciate any help anyone can give (I'd really appreciate a
solution).

Thanks in advance,
-- Jon
--
Jon Leivent
MS A156
The MITRE Corporation
202 Burlington Road
Bedford MA, 01730-1420

email: jil@mitre.org
tel: (617) 271-7648
fax: (617) 271-3816
Newsgroups: sci.math.stat
From: A735FJO@HASARA11.BITNET
Newsgroups: sci.math.stat,sci.math
Subject: Re: sampling-simulation
Date: 16 Apr 92 07:18:58 GMT
Organization: SARA - Stichting Academisch Rekencentrum Amsterdam

Dear readers,
If this is the wrong newsgroup, please forgive me.
Not being a mathematician, I have the following question:
What is the best computer program for doing mathematics.
I've seen REDUCE and DERIVE, and I've heard of MATHCAD.
I use DOS on an IBM-compatible PC.
What program is the most powerful,
and what program is easy to use?
 
Thanks in advance,
 
- Frans Oort (a735fjo@hasara11.bitnet)