As from this post as @Ben Bolker pointed out that :
.. note that these (as often pointed out by Doug Bates) the Wald standard errors are often very poor estimates of the uncertainty of variances, because the likelihood profiles are often far from quadratic on the variance scale ...
I have the following questions :
(1) If the likelihood profiles are often far from quadratic on the variance scale , does it imply the Wald confidence interval has a very poor chance to contain the true parameter value ?
(2) Why are the Wald standard errors often very poor estimates of the variances ? (Don't know whether there is any technical difference between "estimates of the variances" and "estimates of the uncertainty
of variances") .