Unbiased Time-Average Estimators for Markov Chains
提出一种对马尔可夫链功能的时间平均估计量进行修正的方法，得到无偏估计量，并证明其平方可积、期望运行时间有限，在波动率预测、排队论和高维高斯向量模拟中有应用。
We consider a time-average estimator f k of a functional of a Markov chain. Under a coupling assumption, we show that the expectation of f k has a limit μ as the number of time steps goes to infinity. We describe a modification of f k that yields an unbiased estimator [Formula: see text] of μ. It is shown that [Formula: see text] is square integrable and has finite expected running time. Under certain conditions, [Formula: see text] can be built without any precomputations and is asymptotically at least as efficient as f k , up to a multiplicative constant arbitrarily close to one. Our approach also provides an unbiased estimator for the bias of f k . We study applications to volatility forecasting, queues, and the simulation of high-dimensional Gaussian vectors. Our numerical experiments are consistent with our theoretical findings.