A NONPARAMETRIC MULTI-STEP PREDICTION ESTIMATOR IN MARKOVIAN STRUCTURES

In this paper, a multistage kernel smoother is proposed to estimate the conditional mean E(Z | X) in a Markovian structure where the observations (Xi,Yi,Zi) are i.i.d. samples from a distribution that possesses the Markov prop- erty E(Z | Y,X )= E(Z | Y ). We prove that the asymptotic mean squared error of the proposed estimator is smaller than that using the Nadaraya-Watson estimator directly on the pairs (Xi,Zi). A simulation study is also given.