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Exact estimation techniques provide a means to construct an unbiased estimator using a sequence of biased estimators. One possible application of this is in obtaining unbiased approximations of expectations with respect to Markov chain stationary distributions. In this case, the methodology exploits a coupling of two Markov chains to produce an estimator possessing the correct expectation.

Exact estimation for Markov chains
In the case of a Markov chain $$(X_n)_{n\ge 0}$$, the objective of exact estimation techniques is to provide for some test function $$h$$ an estimator $$H(h)$$ such that $$\mathbb{E}[H(h)]=\mathbb{E}[h(X_\infty)]$$. The following provides an example construction of exact estimation for Markov chains.

We assume that there exists two Markov chains $$(X_n)_{n\ge 0}$$ and $$(Y_n)_{n\ge 0}$$ such that for any $$n$$, $$X_n \stackrel{d}{=} Y_n$$ and in addition we assume that there exists a finite (a.s.) meeting time $$\tau$$ such that $$\forall n\ge \tau$$ we have $$X_n=Y_{n-1}$$.