This paper is the second part of our study on the non-parametric estimation of MS-NAR processes started with [L. Fermin et al. 2017]. We consider the Nadaraya-Watson type regression function estimator for non-linear autoregressive Markov switching processes. In this context the regression function estimator is interpreted as a solution of a local weighted We have introduced, in the first work, a restoration-estimation Robbins-Monro algorithm to approximate the estimator, and we proved identifiability of model and the consistency of the non-parametric estimator. In this work, we obtain the central limit theorem for the non-parametric estimator, whether the Markov chain is observed or not. Finally, we present a detailed simulation study illustrating the performances of our estimation procedure.

翻译：本文是继[L. Fermin等人，2017]之后关于MS-NAR过程非参数估计研究的第二部分。我们考虑针对非线性自回归Markov切换过程的Nadaraya-Watson型回归函数估计量。在此背景下，回归函数估计量被解释为局部加权方程的解。在第一项工作中，我们引入了一种恢复-估计Robbins-Monro算法来近似该估计量，并证明了模型的可识别性以及非参数估计量的一致性。在本工作中，我们获得了非参数估计量的中心极限定理，无论Markov链是否被观测到。最后，我们通过详细的模拟研究展示了估计过程的性能。