Abstract: 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 property 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.
Key words and phrases: Kernel smoothing, mean squared errors, multi-stage smoother.