Estimation for Markov chains with periodically missing observations
研究了当时间序列在固定周期点缺失观测时，如何改进非参数估计量，通过添加无偏估计量来降低方差，并以有限状态空间的一阶马尔可夫链为例，用模拟展示了新估计量的优异表现。
When we observe a stationary time series with observations missing at periodic time points, we can still estimate its marginal distribution well, but the dependence structure of the time series may not be recoverable at all, or the usual estimators may have much larger variance than in the fully observed case. We show how non‐parametric estimators can often be improved by adding unbiased estimators. We focus on a simple setting, first‐order Markov chains on a finite state space, and an observation pattern in which a fixed number of consecutive observations is followed by an observation gap of fixed length, say workdays and weekends. The new estimators perform astonishingly well in some cases, as illustrated with simulations. The approach extends to continuous state space and to higher‐order Markov chains.