• Bootstrap

    From waleedsial@gmail.com@21:1/5 to Rich Ulrich on Sun Nov 25 18:52:18 2018
    On Tuesday, 4 March 2014 19:18:59 UTC-6, Rich Ulrich wrote:
    On Mon, 3 Mar 2014 15:15:52 -0800 (PST), varinsacha@yahoo.fr wrote:

    Hi,
    It is me again !

    I have 2 questions this time about bootstrap.
    Many thanks for your precious help.

    1) One way of carrying out the bootstrap is to average equally over all possible bootstrap samples from the original data set (where two bootstrap data sets are different if they have the same data points but in different order). Unlike the usual
    implementation of the bootstrap, this method has the advantage of not introducing extra noise due to resampling randomly.
    To carry out this implementation on a data set with n data points, how many bootstrap data sets would we need to average over?


    If you are referring to the usual sort of bootstrap,
    where N cases are drawn with replacement from the
    sample of N, then "all possible samples" is N raised to
    the Nth power.

    An N of 10 is nearly the max, for modern computers.

    Depending on what statistics you are bootstrapping,
    you might have to figure what you want to do for
    those exceptional samples where the same case is
    drawn all 10 times.


    2) If we have n data points, what is the probability that a given data point does not appear in a bootstrap sample?

    The chance that it is not drawn first is (1-1/N).
    Ditto, for each next draw; so raise that quantity to N.

    --
    Rich Ulrich

    I dont understand the 2nd part where Professor ulrich said to raise that quantity to N.
    I understand that the probability of getting in draw is 1/N and not getting will be 1-1/N
    But I dont get what do we mean by raising it to N

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  • From David Duffy@21:1/5 to waleedsial@gmail.com on Fri Nov 30 03:29:45 2018
    waleedsial@gmail.com wrote:
    2) If we have n data points, what is the probability that a given
    data point does not appear in a bootstrap sample?

    The chance that it is not drawn first is (1-1/N).
    Ditto, for each next draw; so raise that quantity to N.

    --
    Rich Ulrich

    I dont understand the 2nd part where Professor ulrich said to raise
    that quantity to N. I understand that the probability of getting in
    draw is 1/N and not getting will be 1-1/N But I dont get what do we
    mean by raising it to N

    How many draws are needed to make one bootstrap sample?

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