This design document works out details of approximate maximum likelihood estimation for aster models with random effects. Fixed and random effects are estimated by penalized log likelihood. Variance components are estimated by integrating out the random effects in the Laplace approximation of the complete data likelihood (this can be done analytically) and maximizing the resulting approximate m...

Standard methods frequently produce zero estimates of dispersion parameters in the underlying linear mixed model. As a consequence, the EBLUP estimate of a small area mean reduces to a simple regression estimate. In this paper, we consider a class of generalized maximum residual likelihood estimators that covers the well-known profile maximum likelihood and the residual maximum likelihood estim...

A very popular form of hypothesis test is the likelihood ratio test, which is a generalization of the optimal test for simple null and alternative hypotheses that was developed by Neyman and Pearson (We skipped Neyman-Pearson lemma because we are short of time). The likelihood ratio test is based on the likelihood function fn(X−1, · · · , Xn|θ), and the intuition that the likelihood function te...