Evaluation of convergence rate in the central limit theorem for the Kalmanfilter

State space models are used for modeling of many physical and economic proc esses. An asymptotic distribution theory for the state estimate from a Kalm an filter in the absence of the usual Gaussian assumption is presented in [ 1], They proved the central limit theorem for state estimators when the ran dom terms in the model have arbitrary distribution. In this study, some con vergence rates in the central limit theorem are given. These convergence ra tes are used for the development of a nonparametric test of the validity of the model.