Semiparametric nonlinear mixed-effects (NLME) models are flexible for modeling complex longitudinal data. Covariates are usually introduced in the models to partially explain interindividual variations. Some covariates, however, may be measured with substantial errors. Moreover, the responses may be missing and the missingness may be nonignorable. We propose two approximate likelihood methods for semiparametric NLME models with covariate measurement errors and nonignorable missing responses. The methods are illustrated in a real data example. Simulation results show that both methods perform well and are much better than the commonly used naive method.

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In this paper, the state estimation problem for discrete-time linear systems influenced by multiplicative and time-correlated additive measurement noises is considered where the multiplicative noises are zero-mean white noise sequences, and the time-correlated additive noise is described by a linear system model with white noise. An optimal linear estimator for the system under consideration is proposed, which does not require computing the inverse of state transition matrix. The proposed estimator has a recursive structure, and has time-independent computation and storage load. Computer simulations are carried out to demonstrate the performance of the proposed estimator. The simulation results show the superiority of the proposed estimator.

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This paper considers the problem of simultaneously testing a non-hierarchical finite family of hypotheses. Several definitions have been introduced. They are used to shed interesting light on the interrelationship between the four types of test that have previously been proposed.

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