AI-GEOSTATS: How biased are LS estimates of variogram parameters?
- This may be a naive question, but one that I cannot get a clear answer
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,
Dept. of Biology
Dalhousie University, B3H 4J1
Halifax, Nova Scotia, Canada
Office: LSC 800
phone: 902 494 3910
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