It is difficult to know what to advise.  You do not describe why you are
sampling in the first place, nor what characteristics you want the
sample to have, nor whether the order in which you list the elements of
a set is some "natural" order, or a haphazard order, or an order that
you have already randomized;  for instance.

You also mention a "sliding window protocol";  the term is not familiar
to me (it may be to others), and while I can imagine what it might
entail, that might not be at all what you had in mind.  (On the face of
it, though, it does not appear to be a device likely to yield a sample
that one could reasonably call "random".)

On 20 Dec 2002, ABC wrote:

> I would like to use so-called sliding window protocol to do the
> sampling. Namely, I do not want to do the complete analyis, so I use
> the sliding window as a substution. Here is an example.
>
> Let we have some element in a set.
> {e1, e2, e3, e4, e5, e6, e7, e8, e9, e10}
>
> Suppose I need to take 3 of them to form a subgroup at a time, the
> total combinations of should be 10 C 3, i.e. 120. This number is
> still managable. However, if the data set become larger, it must be
> impossible to have a complete consideration. Therefore, I choose the
> sliding window protocol to overcome this.

Why not simply sample at random from the original set of 10 elements,
without replacement?  That would make all possible triples of elements
members of your sampling universe, and each triple would have equal
likelihood of being selected:  which I would suppose to be one of your
goals.

> Could you give me some suggestions to solve this? I just think of 1
> solution of randomizing the original set first and slide the windows
> afterwards. Even doing that I am afraid this is not a good way,

I am inclined to agree with you.

> a good sampling of the data set.

HTH.    -- DFB.
 -----------------------------------------------------------------------
 Donald F. Burrill                                            [EMAIL PROTECTED]
 56 Sebbins Pond Drive, Bedford, NH 03110                 (603) 626-0816
 [was:  184 Nashua Road, Bedford, NH 03110               (603) 471-7128]

.
.
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