From: Allen Keesee [mcomlgl@bigpond.com.kh]
Sent: Thursday, June 28, 2001 12:23 AM

Have read Wilcox 3 and 4, and 
would like to offer following
comments/questions (references are to Wilcox page nos.):



Chapter 3:


    32) 12th line from bottom (and  p 42, 7th line fr bottom, and p55, 17 fr
bott, and other places)   --  the practice of using "then" to start the
second clause of a sentence that has begun with "if" is (from an English
grammar class pt of view) I believe incorrect syntax. Nor (from the examples
I am familiar with) can it be written off as an attempt at consistency with
"prevalent" programming language structure since while SAS uses the "if....
then" structure, neither C++ (just "if.. else if... else..." etc., no "then"
involved), nor S+ (if  and if else) does.
            Also NB that Wilcox does not always use "then" after "if": cf, p
65, 7th and 8th lines fr top).


    36)  I may be misreading but I believe the eqn at top this pg should 2 -
8 and 4 - 8, not 2 - 7 and 4 - 7 and that some of the other numbers are
wrong because of this 7 vs 8 mix up;


    37) 5th and 6th lines down  --  and 37) box-plot method of defining
outliers  --  Seems any across-the board rule re outlier characterization is
inappropriate.. Would think what constitutes an "outlier", because the term
seems to carry the implication that any such observation is a candidate for
down-weighting (e.g., via GLS, in the sense that outliers in a series of Y
observations for a given X value will are down weighted when the mean-Y they
are associated with is down-weighted) or outright exclusion from
consideration (e.g., via trimming means),  should depend on the nature of
the data being looked at.

            There are many situations, that is, where what might by any
formula such as those ref'd above (2 std devs, or "outer quartile + 1.5 *
IQR") might be called an "outlier" was nevertheless of central import and
far from being up for trimming or de-emphasis, might be at the heart of a
certain calculation or judgment.

    Flood plane boundaries, it is my understanding are based on "100 yr high
level " estimates  --  and affect real estate values significantly. Admiral
Bull Halsey, despite his theretofore brilliant record had his career cut
short (and  was almost court martialed) because in 1945 of having let the (I
think  it was ) Third Fleet run afoul  (with significant losses of men and
ships) of two major typhoons (one off Leyte, the other off Okinawa) in the
space of about 6 months  --  i.e., there, the fact that being in the path of
two such storms in  6 months might  have been an "outlier-ish" event was in
no way viewed as by the Navy grounds for exoneration from blame.

    And Long Term Cap Mgmt from one account  I have read owed its demise
most directly (although with other contributing factors) to the fact that
the main interest rate spread model put together by its chief model builder
ruled out the possibility of any event which could be more than 6 std devs
away from the mean.



    38)  first 2 lines  --  not clear why having "extreme" values in far
less than 25% of observations would not a) alter position of 25th and 75th
quartiles and thus b) alter the definition of "outlier" since this def
depends on the value  of the IQR, and hence c) cause "masking".


    39) Does curve of sample mean values become "more normal" (i.e., better
and better approximate normal) ONLY as size used for the samples ("n")
increases or ALSO as number of samples, each generating one sample mean
value, increases? I.e., if you had a small sample size "n" but a large
number of  samples, would you get "just as normal a curve (of the means of
the respective samples)" as if you had a much smaller number of samples but
each sample was of a much larger size (larger "n"; the central limit theorem
case I believe)?

         I ask this because although it seems clear CLT deals only with size
of "n",  Wilcox repeatedly implies the number of samples (not clear whether
"in addition to" or "instead of"  their common individual size, "n") is what
brings the result curve close to normal, Cf,  p 51: "... if we could repeat
an experiment billions of times, we would get fairly good agreement between
the plot of weighted means and the normal curve."


    45) 9th line fr bott  --  "... convergence to normality is quicker when
using medians."  --  "quicker" as used here seem to mean, "with fewer
observations"; is this interpretation (of "quicker" by me) correct?


Chapter 4:


     50) 15th and 4th from bott  --  Does use of MSE as criteria for
evaluating accuracy of  ways of various ways of using sample means to
estimate pop means require knowledge of what pop mean actually is?

            If so, what do you use for such evaluation where the pop mean is
not known?


    53)  --  8th and 7th from bott  --  Doesn't this stmt re the mean being
the "optimal" estimator "for any probability curve we might consider" assume
that normalcy is a more prevalent condition than nonnormalcy?

        And isn't such an assumption unproven/dubious/unlikely-to-be-true,
or is he just talking about curves generated by a CLT large sample-size
sampling procedure?


    56) 12th fr top  --  Fig 4.2 line more like y = x -10 than y = x + 10.


    56) 9th fr bott  --  "... among all the weighted means we might
consider..."  --  what are examples of systems other than OLS for developing
a series of weighted means, and on what basis (for what benefit) might one
think to consider them?


    58) 13 fr bott  --  "frequentist approach" undefined/unexplained.


            Regards,



AK