[R] non positive-definite G matrix in mixed models: bootstrap?

[Bruno L. Giordano]

Dear list,
In a mixed model I selected I find a non positive definite random effects 
variance-covariance matrix G, where some parameters are estimated close to 
zero, and related confidence intervals are incredibly large.

Since simplification of the random portion is not an option, for both 
interest in the parameters and significant increase in the model fit, I 
would like to collect "unbiased" random effects estimates.

I used bootstrap to this purpose, creating a linear model for each cluster 
and bootstraping the variance of the coefficients. Is this procedure 
reasonable? Would it be reasonable in this case to keep the marginal portion 
of the mixed model?
Note that in presence of positive-definite G matrix this bootstrap approach 
and the mixed effect model give highly similar estimates and that in the non 
positive-definite model the bootstrap and mixed model marginal-model 
estimates are highly similar as well.

Thank you
    Bruno