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AI-GEOSTATS: How biased are LS estimates of variogram parameters?

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  • Dan Kehler
    This may be a naive question, but one that I cannot get a clear answer to. Lahiri et al. (J. of Stat. Plan. and Inf. 2002) state that least squares estimates
    Message 1 of 1 , Feb 15, 2004
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      This may be a naive question, but one that I cannot get a clear answer
      to.

      Lahiri et al. (J. of Stat. Plan. and Inf. 2002) state that least squares
      estimates of variogram parameters are asymptotically consistent. My own simulation
      results indicate that least squares estimates are plagued by biases that
      do not decrease with even up to 300 observations of a zero-mean spatial
      random field. This initially suggested a problem with the simulations, but
      simulations by Pardo-Iguzquiza (Comp. & Geosc. 1999) also show some
      serious biases that do not always decrease with sample size.

      Muddling through the literature suggests that since the MOM estimator of
      the empirical variogram is asymptotically unbiased, then the variogram
      parameters estimated by least squares share the same property.

      Is the strong bias I and others have encountered an artifact of the
      non-linear least squares algorithm (in my case, fitting an exponential
      variogram), or is it a real problem with even sizable samples?

      A straight maximum likelihood approach to estimate the covariance matrix
      directly seems to relatively unbiased for moderate sample sizes, and
      avoids the extra steps of estimating the empirical semivariogram,
      worrying about weights, distance categories, minimum pair requirements,
      maximum distance cutoffs etc...

      Any insight would be appreciated,

      Cheers,

      Dan Kehler



      ____________________________________
      Daniel Kehler
      Dept. of Biology
      Dalhousie University, B3H 4J1
      Halifax, Nova Scotia, Canada
      Office: LSC 800
      email: kehler@...
      phone: 902 494 3910




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