In article <a44tnt$l4e$[EMAIL PROTECTED]>,
Michael Hochster <[EMAIL PROTECTED]> wrote:
>Here are my thoughts on this. The most important mathematical
>requirements are calculus, real analysis, and linear algebra.
>You need to to know these topics thoroughly. Whatever
>textbooks are used for undergraduate math majors wherever you
>are are probably fine. You also need to know non-measure
>theoretic probability at the level of a book like Pitman's
>Probability.
It is unfortunate that rigorous measure theory, without the
complicated proofs, is not done earlier. One can easily
do it at the high school level; sigma-fields are not that
essential even for countable additivity, which is needed
for the Radon-Nikodym Theorem, which is basic for statistics.
Measure theory is probability without it being assumed that
the whole space has measure 1. Integration is nothing more
than sums of products and limits of such, and even at the
undergraduate level, such as Pitman, the limits needed are
countable limits. This gets the full "Lebesgue" integral,
without starting with Lebesgue measure.
>Despite Herman Rubin's admonitions against weak courses, I think
>it is very useful to know some "basic" statistics at the level
>of Rice's "Mathematical Statistics and Data Analysis" or DeGroot's
>"Probability and Statistics." A very concise overview of statisical
>theory is Silvey's book, which I think may be called "Statistics."
The only one of these with which I am familiar is the one
by DeGroot. It is reasonable, but I believe that someone
with a decent real analysis course at the undergraduate
level can do much better than this initially. Little, if
anything, is gained by lowering the level. Of course, one
is likely to do better having that before, as most of the
course will be a repetition, although the lack of generality
may work in the opposite direction.
I would tend to reject any book which does data analysis;
I consider cookbook statistics to be putting a loaded gun
in the hands of an someone who is totally ignorant about
guns; not necessarily an idiot, as the idiot cannot learn.
For data analysis, change "gun" to "armed nuclear weapon".
>If you don't have exposure to statistics at least at this level,
>you may have trouble understanding the motivation for many things
>you do in first year courses. I had this problem myself.
The bigger problem is that you may have received
misconceptions. This is not that surprising; it was in
1933 that Neyman pointed out that "significance level"
did not mean what they thought it meant, and those who
have started out with methods have great difficulty in
avoiding the same misconception. Even many graduate
level courses teach statistics as religion.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
[EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558
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