Evaluation of convergence rate in the central limit theorem for the Kalman filter

State-space models are used for modeling of many physical and economic processes. An asymptotic distribution theory for the state estimate from a Kalman filter in the absence of the usual Gaussian assumption was presented by Spall and Wall (1984). They proved the central limit theorem for state estimators when the random terms in the model have arbitrary distribution. In this study, some convergence rates in the central limit theorem are given. These convergence rates are used for the development of a nonparametric test of the validity of the model.