test significance of nugget variance
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Wald test for nugget variance in summary output of an SVC_mle object: Is this sensible?
You used 'W' for Wald, I see. I presumed it was a likelihood ratio test framework.
For Wald, the p-value is (somewhat) equivalent to the standard error or CI.
The question is rather, Wald test for the other variance parameters sensible?
I presume (here to be discussed), that it would be more sensible to look at estimated likelihoods and derive CI for these. That means, your likelihood function is built up, plug-in all estimates and get the bounds. With this approach, you could also provide the CI for the range parameters. Computationally, it is quite straightforward and fast.
I think I brought this up some time ago, I wonder if an individual or all SVCs could be tested with generalized LRT (Held and Sabanes Boves, 5.5). Much should cancel...
Are there any studies that compare the finite sample properties of Wald and LR tests for mixed effects / GP models?
Not that I know of... but I have not checked in years...
There are some permutation tests for overall dependency. Refs in https://doi.org/10.1007/978-3-030-57306-5_45 are not much of a help either.