Non Parametric Signal Interpolation
This paper considers the problem of interpolation (smoothing) of a partially observable Markov random sequence. For the dynamic observation models, an equation for the interpolation of the posterior probability density is derived. The main goal of this paper is to consider the smoothing prob lem for the case of unknown distributions of an unobservable component of a random Markov sequence. Successful results were obtained for the strongly stationary Markov processes with mixing and for the conditional density be longing to the exponential family of densities. The resulting method is based on the empirical Bayes approach and kernel nonparametric estimation. The equation for the optimal smoothing estimator is derived in the form indepen dent of unknown distributions of an unobservable process. Such form of the equation allows to use the nonparametric estimates for some conditional func tionals in the equation given a set of dependent observations. To compare the nonparametric estimators with optimal mean square smoothing estimators in Kalman scheme, simulation results are given.