Inference of nonlinear mixed models for clustered data under moment conditions

Abstract

Two statistical inference problems in nonlinear mixed models (NLMM) are considered under only moment conditions on random effects and random errors. First, higher-order moment estimates of random effects and random errors in NLMM are proposed and they turn out to be strongly consistent. Second, a difference-type test $$T_{mDs}$$ is developed to test whether some sub-vector of random effects exists or not, which is easy to implement without requiring the Monte Carlo method. Its theoretical properties including the power properties are obtained. Moreover, in the special case of testing the existence of random effects, two kinds of tests are also constructed: the global difference-type test $$T_{mDG}$$ , which is a special case of $$T_{mDs}$$ , and the modified score-type test $$ST_{n0}$$ , which is motivated by $$ST_{nru}$$ in Russo et al. (TEST 21:519–545, 2012). The simulation study indicates that $$T_{mDs}$$ is the most powerful. A real data analysis is also conducted to investigate the applicability of the procedures.