[R-sig-Geo] Analytical covariance expression of backtransformed Box-Cox data

[Anders Malmberg]

Dear Readers,

I have a question not related to R itself. It is of a theoretical 
nature. I hope this
is ok.

I am facing the problem where some spatial data follows the Gaussian 
distribution
after a Box-Cox transformation. I am using geoR and I understand that 
geoR (in the latest version)
for lambda \neq 0 or 0.5 calculates the mean and variance through simulation
(using backtransform.moments()).

If X is original data and Y is Box-Cox transformed data for which I have
estimates of the parameters in exponential covariance function, then
it should be that (mean=0),

cov(X_i,X_j)=E(X_i X_j) = E(f(Y_i) f(Y_j))

where "f" is the inverse of the Box-Cox transform. But this turns out to 
be quite messy.
Is it possible to find an analytical expression for any lambda?

Thanks in advance,

Anders