| I have read the first article. I have the second sitting next to my
bed waiting to be read. I'll get back to you on that one.
I found the first article rather disappointing. The area of "computer
intensive statistical methods" is an important one. The article
unfortunately pushed rather too strongly one of the most glamorous but
least useful of those techniques -- the bootstrap which was invented by
Efron. Someday the bootstrap (and its relative "the jacknife) may be a
broadly useful technique, but right now nobody knows when its results
can be considered valid and when they can't except for some special
cases. If you get an answer via the bootstrap you are generally open
to the criticism that the assumptions that it is based on may not apply
(since no one knows when they apply and when they don't) and that your
results therefore don't mean anything.
There was a rather downplayed reference to the problem but it was
essentially dismissed. ("Theoretical work on properties of the
bootstrap is proceeding at a vigorous pace. We have empahsized
standard errors here, but the main theoretical thrust has been toward
confidence intervals. Getting dependable confidence intervals from
bootstrap calculations is challenging, in theory and in practice, but
progress on both fronts has been considerable"). In fact the primary
problem which needs to be addressed with bootstrap techniques applies
to any application of them.
The bootstrap assumes that sample taken from the population is
"representative" of that population in a very general way. Clearly
this is true when the sample is large enough, but just what is large
enough? If the population distribution is simple and well-behaved,
(e.g., normal) the answer is probably that a fairly small sample is
good enough. But what if the distribution is in some sense very lumpy
(even fractal) in character and the statistic you are bootstrapping is
sensitive to that lumpiness? You obviously need enough samples so that
the "lumps" are reflected in the sample distribution. How do you
decide what is a good enough sample without making the kind of
prior assumptions about the population that the bootstrap is supposed
to allow you to avoid. Generally the amount of analysis required to
justify the bootstrap in any particular case is greater than the
amount needed to apply other techniques (both conventional and computer
intensive).
The article then goes on to discuss "nonparametric regression" which
is just a fancy name for data smoothing. The technique is virtually
useless for formal statistical inference, and needs to be used very
carefully for informal statistical inference. It is highly useful
for showing underlying structure of data, but may create the structure
it shows. It is therefore handy for descriptive purposes (data
reduction), for exploratory data analysis and for presentation, but
Efron and Tibshirani don't make clear its limitations. (Reading this
section did, however, make me think of a computer intensive method
which could more legitimately be called "nonparametric regression".
I wonder if anyone else has thought of it? I'm going to have to give
it some more thought to see if it is worth pursuing).
The next technique discussed was "generalized additive models". It is
not a technique I'm familiar with. It seemed interesting, but there
really was not enough information to make much of a judgement. There
was a reference to a book (co-authored by Tibshirani) on the subject
which I may look up, but the account in the article was much to brief
to be useful. If I wasn't interested in new statistical techniques for
there own sakes, I would probably not bother to check the reference.
There was not enough information to allow a reader to decide whether
the technique even might solve a problem that she was facing as a
scientist or engineer.
They then discuss, in somewhat more detail, a kind of clustering
algorithm called CART (Classification and Regression Trees). The
technique was interesting but obviously suffers (as all known
clustering algorithms suffer) from making rather strong assumptions.
The article was rather unclear about when (or if) this technique
is more useful than any other classification/clustering technique
(almost all of which might be called "computer intensive").
It seems to me that anyone reading this who knew statistics but who
didn't know much about these "unconventional" techniques would be left
saying "interesting but so what?"
As I said, disappointing.
Topher
|
| I agree with .2 on the Jackknife and Bootstrap.
"generalized additive models" is a chapter in experimental design
which shows that linear models are more robust than the normality
assumptions usually used to develop the theory would suggest.
Efron was very active 25 years ago in the same areas. I won't bother
to include my speculative opinions of what that implies.
... >(Reading this
>section did, however, make me think of a computer intensive method
>which could more legitimately be called "nonparametric regression".
...
Let me think about this one.
Dick
|
| RE: .3 (Dick)
> >(Reading this
> >section did, however, make me think of a computer intensive method
> >which could more legitimately be called "nonparametric regression".
> ...
>
> Let me think about this one.
I should clarify a bit.
Traditional regression is a bunch of different techniques which are
used for a number of different purposes.
One of those purposes is to fit a "summarizing" curve to a set of
numeric data. There are many non-regression -- indeed, non-
"statistical" -- techniques for this, so I don't really feel that this
is essentially "regression". This is what "loess," the technique in the
article, does.
Another use of regression -- in some ways the primary one -- is to
estimate the values of the parameters of a stochastic numeric model.
Any technique which did this, I think, could legitimately be called an
extension to regression. Its a bit hard to imagine how any technique
for estimating parameters could be considered "non-parametric", though.
Some genetic algorithm techniques which have been used (which "breed"
arbitrary formulae to fit data) come close, but hidden inside there is
a "parametric" model implicit in the fitness criteria.
That leaves, of the major uses of regression that I can think of, only
using regression to answer the question as to whether or not there
exists a relationship between numeric variables. The article didn't
directly suggest any way to do this "non-parametrically", but it did
lead me to ask the question as to whether such a method existed. Since
asking the right question is often the main part of answering it, the
raw outline of a possible procedure occurred to me. Chances are
someone else has already thought of it, and it still needs a lot of
fleshing out, but its fun to think about such things.
Topher
|