We analyze a simple prefiltered variation of the least squares estimator for
the problem of estimation with biased, semi-parametric noise, an error model
studied more broadly in causal statistics and active learning. We prove an
oracle inequality which demonstrates that this procedure provably mitigates the
variance introduced by long-term dependencies. We then demonstrate that
prefiltered least squares yields, to our knowledge, the first algorithm that
provably estimates the parameters of partially-observed linear systems that
attains rates which do not not incur a worst-case dependence on the rate at
which these dependencies decay. The algorithm is provably consistent even for
systems which satisfy the weaker marginal stability condition obeyed by many
classical models based on Newtonian mechanics. In this context, our
semi-parametric framework yields guarantees for both stochastic and worst-case
noise.

通过分析最小二乘估计器的变体，，提出了一种半参数噪声估计算法，可以解决具有偏差，半参数噪声的估计问题，同时可以应用于部分观测线性系统参数的估计，且对于长期依赖问题的方差引入具有可减少的能力.