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Re: [AI-GEOSTATS: Cross Validation - Jackknife (Difference)]

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  • Gregoire Dubois
    Hi Peter, I also found the topic frequently unclear. This is what I understood from my readings. In particular, I would recommnend the following excellent
    Message 1 of 1 , Sep 2, 2003
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      Hi Peter,

      I also found the topic frequently unclear.

      This is what I understood from my readings. In particular, I would recommnend
      the following excellent paper:

      B. Efron and G. Gong, A leisurely look at the bootstrap, the jackknife and
      cross-validation. Am. Stat. 37 (1983), pp. 36–48.

      Maciej Tomczak's paper(ftp://ftp.geog.uwo.ca/GIDA/Tomczak.pdf) is a nice
      presentation of jackknifing and cross-validation that also points the reader
      to the above-mentioned reference.

      As mentioned by Isobel, you could have a look at Cressie's book (Statistics
      for spatial data, Wiley & Sons, revised edition, 1993), in particular pages
      101 and 489-498.

      It results from the above references that, although jackknifing and
      cross-validations are often used in geostatistics to define the same
      technique, they are fundamentally different. Hence, Alexei's Amantov code,
      jackknife.bas, has an incorrect name. It is doing cross-validation.

      The term k-fold cross-validation also sometimes appear... adding more
      confusion.

      In k-fold cross-validation, the data set of the n observed values is divided
      into k training and n-k testing subsets.
      The estimation error of the interpolation algorithm, for example, is then
      obtained from an average measure of the errors over the k tests (e.g. mean
      absolute errors, root mean squared errors).

      The leave-one-out method (what I consider being THE "cross-validation") is a
      particular case in which only one point is used at a time as test set and
      where each point of the data set has been, in turn, removed one time. Here
      again, one will use the average of the n estimations.

      Jackknifing involves pseudo-values and I would reuse Maciej's figure to
      explain the difference between jackknifing and cross-validations.

      Hope this clarifies a bit the issue.

      Gregoire

      PS: if you look at www.scirus.com for the keywords (jackknife) AND
      (cross-validation), you will get 170 peer-reviewed papers. The most recent
      ones can be downloaded at no costs.

      "Peter Pinn" <peterpinn@...> wrote:

      > Hi again,
      >
      > I have a question concernig the jackknife.bas for surfer. In the top line it

      > says:
      >
      > 'Jackknife.bas grids the data set n times, leaving one of the data points
      > out
      > ' each time. Also known as cross-validation. TB - 09 Aug 00.
      >
      > In Maciej Tomczaks paper of SIC´97 I saw the diagram of his algorithm. He
      > distinguished between cross-validation and jackknifing. The above mentioned

      > script says jackknifing is also known as cross-validation. I am very
      > confused about that. Can anyone explain to me what is the result of gridding

      > with the jackknife.bas. Does the result differ from using the
      > cross-validation in surfer ?
      >
      > Finally: Are there any reliable tools for both analysis strategies in
      > commercial software other than surfer ?
      >
      > Thanks in advance,
      >
      > Peter
      >
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