Efficient Estimation of Transition Probabilities in a Markov Chain
马尔可夫链转移概率的有效估计
Let $\{X_1, \cdots, X_N\}$ be $N$ observations on an $m$-state Markov chain with stationary transition probability matrix $\mathbf{P} = (p_{ij}), p_{ij} > 0, i,j = 1,\cdots, m$, where $N$ is a random variable. For any parametric function of $\mathbf{P}$, the information inequality gives a lower bound on the variance of an unbiased estimator; attaining the lower bound depends on whether the sampling plan or stopping rule $S$, the estimator $f = f(X_1,\cdots, X_N)$, and the…