标题： 非参数隐马尔可夫模型中过滤和边缘平滑分布的一致估计 显示英文标题

标题： Consistent estimation of the filtering and marginal smoothing distributions in nonparametric hidden Markov models

摘要： 在本文中，我们考虑在模型参数未知并被估计量替代时，非参数有限状态空间隐马尔可夫模型（HMMs）中的滤波和平滑递归。我们提供了一个显式且时间一致的滤波和平滑误差控制，作为参数估计误差的函数。我们证明了滤波和平滑误差的风险可能被估计量的风险统一上界所限制。最近已经证明，有限状态空间非参数HMMs的统计推断是可行的。我们研究了在参数设置中开发的最近谱方法如何扩展到非参数框架，并给出了非参数谱估计量的L2风险的显式上界。当观测空间是紧致时，这提供了总变差范数下滤波和平滑误差的显式速率。通过模拟数据评估了谱方法在观测条件分布（非参数）和边缘平滑分布估计中的性能。 显示英文摘要

摘要： In this paper, we consider the filtering and smoothing recursions in nonparametric finite state space hidden Markov models (HMMs) when the parameters of the model are unknown and replaced by estimators. We provide an explicit and time uniform control of the filtering and smoothing errors in total variation norm as a function of the parameter estimation errors. We prove that the risk for the filtering and smoothing errors may be uniformly upper bounded by the risk of the estimators. It has been proved very recently that statistical inference for finite state space nonparametric HMMs is possible. We study how the recent spectral methods developed in the parametric setting may be extended to the nonparametric framework and we give explicit upper bounds for the L2-risk of the nonparametric spectral estimators. When the observation space is compact, this provides explicit rates for the filtering and smoothing errors in total variation norm. The performance of the spectral method is assessed with simulated data for both the estimation of the (nonparametric) conditional distribution of the observations and the estimation of the marginal smoothing distributions.