+ Reply to Thread
Results 1 to 3 of 3

Thread: bootstrap theory reference?

  1. #1
    Points: 605, Level: 12
    Level completed: 10%, Points required for next Level: 45

    Location
    UK
    Posts
    60
    Thanks
    11
    Thanked 9 Times in 9 Posts

    bootstrap theory reference?



    I am curious about bootstrap methods, and just read the very elementary explanation of them here:
    http://bcs.whfreeman.com/ips5e/conte...df/moore14.pdf
    It is very interesting to read, but leaves me with a lot of questions. For instance, the
    claim is that the bootstrap distribution approximates the shape and spread of the full sampling distribution. But this is obviously not true in complete generality--you can certainly choose a pathological sample from a population that will yield a bootstrap
    that doesn't approximate either one at all well. So how can this be quantified?
    Are there any theorems along the lines of the following? "Given an underlying distribution satisfying properties A, B, C, and a statistic satisfying properties D, E, and F, the probability of obtaining a sample of size n for which the sampling distribution is within some distance of the bootstrap distribution (appropriately shifted) in some appropriate sense."
    or,
    "given an underlying distribution satisfying properties A,B, C, and
    a statistic satisfying D, E and F, then as n->infinity,
    the bootstrap distribution for (all but a set of samples whose measure shrinks to 0) approaches the sampling distribution of size n in some appropriate sense."

    Alternatively, are there simulations that suggest the bootstrap works well in various situations? When doesn't it work well (other than for small samples, of course)?
    Are there particular statistics or underlying distributions for which it is known to
    go way off?

    Is there a good reference for this that isn't 200 pages long and containing 256923452365432345 different variable names (which is what most of the books in my area of maths are like--but I am doing this for recreation!)?
    Last edited by Eugenie; 08-19-2012 at 01:41 PM.

  2. #2
    Super Moderator
    Points: 8,575, Level: 62
    Level completed: 42%, Points required for next Level: 175
    Dragan's Avatar
    Location
    Illinois, US
    Posts
    1,725
    Thanks
    0
    Thanked 127 Times in 113 Posts

    Re: bootstrap theory reference?

    I would say that a good book to read on this matter, and to address your concerns, would be start with:

    Efron, B., Tibshirani, R. J. An Introduction to the Bootstrap. Chapman & Hall/CRC.

  3. The Following 3 Users Say Thank You to Dragan For This Useful Post:

    Dason (08-23-2012), Eugenie (08-24-2012), Lazar (08-23-2012)

  4. #3
    Points: 1,980, Level: 26
    Level completed: 80%, Points required for next Level: 20
    derksheng's Avatar
    Posts
    247
    Thanks
    49
    Thanked 34 Times in 28 Posts

    Re: bootstrap theory reference?


    If you're into bootstrap regressions, you can't beat "Bootstrap Tests for Regression Models". Complete breakdown into categories of exactly which Gauss-Markov violations each bootstrap corrects for.

  5. The Following User Says Thank You to derksheng For This Useful Post:

    Eugenie (08-24-2012)

+ Reply to Thread

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts








Advertise on Talk Stats