A number of variogram models were fitted where estimates like nugget, range, and sill were obtained from gstat of R. Could anyone guide me on how to obtain standard error for each of these estimates? The knowledge of standard error will enable us to determine if the estimate is significantly different from zero. It may also be feasible to compare the estimates among models fitted to the same data for significant differences.
In gstat, the automatic fitting uses least squares but in fact this is not a single choice but several choices, i.e, you can use weighted least squares and there are several different ways to do the weighting. There is no theory to absolutely determine the best weighting nor even whether least squares is best. A number of authors have used some form of maximum likelihood but this implies some distributional assumptions and the data collection plan will not ensure these assumptions. You won't get a standard error for the model parameters from either the fitting statistics nor from cross validation statistics.
You might want to look at the book "model based geostatistics", however it assumes that the data has been transformed to a multivariate gaussian distribution, then the big problem is how to re-transform the kriged values
If the true range is zero this implies a pure nugget effect variogram, the cross validation statistics would provide evidence as to whether a pure nugget model or some other model.is a good choice.
If the sill is zero then all the data values are exactly the same, i.e. there is no variation.
In both cases taking a null hypothesis of zero for the parameter is of little use
Although using least squares to fit a variogram model is somewhat analogous to using least squares to fit a linear regression model there are very important differences, in particular the underlying statistical assumptions are very different
In gstat, the automatic fitting uses least squares but in fact this is not a single choice but several choices, i.e, you can use weighted least squares and there are several different ways to do the weighting. There is no theory to absolutely determine the best weighting nor even whether least squares is best. A number of authors have used some form of maximum likelihood but this implies some distributional assumptions and the data collection plan will not ensure these assumptions. You won't get a standard error for the model parameters from either the fitting statistics nor from cross validation statistics.
You might want to look at the book "model based geostatistics", however it assumes that the data has been transformed to a multivariate gaussian distribution, then the big problem is how to re-transform the kriged values
If the true range is zero this implies a pure nugget effect variogram, the cross validation statistics would provide evidence as to whether a pure nugget model or some other model.is a good choice.
If the sill is zero then all the data values are exactly the same, i.e. there is no variation.
In both cases taking a null hypothesis of zero for the parameter is of little use
Although using least squares to fit a variogram model is somewhat analogous to using least squares to fit a linear regression model there are very important differences, in particular the underlying statistical assumptions are very different
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