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Re:GEOSTATS: ASH - modeling technique

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  • Gerry Whittaker
    ... The Averaged Shifted Histogram (ASH) is a kernel density estimation technique introduced by David Scott, Department of Statistics,Rice University. You may
    Message 1 of 3 , Oct 6, 1997
      >I have seen reference to a modeling method referred to casually as
      >"ASH." I know next to nothing and have only heard mention of this
      >method as a faster substitute to kriging with fewer distortions at the
      >boarders....
      >
      >James D. Long Office: (606)257-7272 ext 271
      >Department of Ag Economics Pager: (606)741-9818
      >University of Kentucky
      >331 Ag Engineering Building E-Mail: jdlong00@...
      >Lexington, KY 40504-0276

      The Averaged Shifted Histogram (ASH) is a kernel density estimation
      technique introduced by David Scott, Department of Statistics,Rice
      University. You may also see references to weighted averaging of
      rounded points (WARP), by Scott and Haerdle. The algorithm proceeds in
      two steps: first the data in binned to a rectangular array, then kernel
      density estimation or nonparametric regression is applied to the binned
      data. The ASH is discussed in detail in "Multivariate Density Estimation"
      by Scott. The ASH density estimation code is available from STATLIB.
      The code is a set FORTRAN routines called by functions in S-PLUS.

      At the Economic Research Service, we have found the ASH to be much
      faster, and generally more robust than other local regression techniques.
      A typical surface will cover the conterminous U.S. with a large number
      of features. Locfit, Loess and kriging do not did not do well in application
      to this data. An additional problem is that the data is from stratified,
      complex design sample surveys. There are no versions of Loess or
      Kriging that can deal with stratification, while the ASH deals with this in a
      simple way. Some results: 535,000 observations of population at the
      block group level from the 1990 census took approximately 15 minutes to
      bin in three dimensions (population, latitude, longitude) to a 600 x 400 grid
      on a pentium 90. The nonparametric regression then took about 5 min.
      There is a description of this work in Scott and Whittaker,"Multivariate
      Applications of the ASH in Regression," Communcations in Statistics,
      v.25, 2551-2530(1996).

      Gerald Whittaker gerryw2@...
      Economic Research Service, USDA
      1301 New York Ave, NW #424
      Washington, DC 20005-4788
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    • J-F Lenain - L.A.S.E.H.
      ... ASH is special case of discretized kernel smoothing technique (WARPING): it use - discretized triangular kernel - same grid for both prebinning (data) and
      Message 2 of 3 , Oct 7, 1997
        >I have seen reference to a modeling method referred to casually as "ASH." I
        >know next to nothing and have only heard mention of this method as a faster
        >substitute to kriging with fewer distortions at the boarders. Could someone
        >point me to where to get information on this procedure.

        ASH is special case of discretized kernel smoothing technique (WARPING):
        it use
        - discretized triangular kernel
        - same grid for both prebinning (data) and postbinning (estimation
        and interpolation).

        estimating with linear interpolation in postbinning (plotting for ex.)
        is quite as accurate as usual kernel estimates: the ratio of bin width
        and kernel window must be <=1/5 in practice.
        HALL and WAND, 1996 : J. of Multivar. Anal., 56, 165-184 (prebinning)
        JONES, 1989 : J. Amer. Stat. Assoc., 84, 407, 733-741 (pre and postbinning)
        SCOTT, 1985 : Annals of Stat. , 13, 3, 1024-1040 (ASH, FP-ASH)

        using FFT for convolution is a very efficient way to compute ASH,
        and easy to program
        SILVERMAN, 1982 : Applied Stat., 31, 93-99
        JONES at al., 1984 : " " , 33, 120-122

        (rem: the above ref. are for density estimates)

        see also:
        HARDLE, 1991 : smoothing techniques - Springer
        for the warping approximation of Nadaraya estimate (p137..)
        (with code)
        SIMONOFF, 1996 : smoothing... - Springer
        for a wide bibliography
        HARDLE et al., 1995 : Xplore - Springer
        is the book of a program using ASH
        you can download Xplore from the web site
        http://www.xplore-stat.de/





        -----------------------------
        jean-francois LENAIN
        L.A.S.E.H.
        faculte des Sciences
        87060 Limoges CEDEX (France)
        e-mail: lenain@...
        -----------------------------

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