A Study Of Sparse Longitudinal Data Statistical Inference Under The State-space Model

In recent years, the research on sparse longitudinal data in mixed-effects models state-space has attracted the attention of many researchers from different fields. Based on dynamic data, the state space model is a dynamic time-domain model with time as the independent variable, which is a powerful tool for the analysis of time series data. Longitudinal data is a cutting-edge issues in current statistics, and the main analytical method is mixed-effects state-space model. In this paper, it is based on a nonlinear mixed-effects state-space model(NLMESSM) with unknown parameters, take target tracking for example and provide very useful information for dynamic of research goals by simulating to generate sparse longitudinal tracking data. Based on nonlinear mixed effect state-space model, we use sequenctial importance resampling(SIR) algorithm and auxiliary particle filter(APF) algorithm to estmate the state variables and the unknown parameter in the model. In this paper, the status of non-linear mixed-effects estimates based on state space model has been studied mainly as follows:1. First introduce the research framework and research status at home and abroad of state-space model, and expounds the definition of the state space model and the mixed effect model. On the premise of the linear state space model, it is introduced the theoretical foundation of Kalman filter algorithm for the sparse longitudinal data.2. Then, for the problem of estimating a nonlinear state space model, introduces the particle filter method and the three processing techniques. Through the analysis of the algorithm, it has advantages of easy sampling and the simple calculation. But the disadvantage is that it isn’t influenced by the observations, and sample with blindness, which leads to particles in relatively large weight may be lost, leaving the weight of most particles is small, and this is not conducive to approximate the true poster density. Through improving the algorithm, introduce the auxiliary particle filter. It overcomes the shortcoming of blind sampling, and at each moment they are updated with the observations at the same time, improving the quality of generated particles.3. Finally the example of target tracking is converted to a nonlinear mixed effects model state space form. In the premise of research on single objective and multi-objective,based on the observing longitudinal data, select the sequential importance resampling( SIR) algorithm and the auxiliary particle filtering(APF) algorithm for the state estimation, and discuss the parameter estimation of signal target. Through the error analysis, compares the advantages and disadvantages of algorithms, and change the influence factors to improve the algorithm accuracy.