Blockwise Empirical Likelihood and Efficiency for Markov Chains
针对任意状态空间上的遍历马尔可夫链，利用分块经验似然权重改进平稳分布线性泛函的经验估计量，并证明该估计量是有效的，同时给出两种渐近等价的加性校正估计量。
ABSTRACT Suppose we observe an ergodic Markov chain on an arbitrary state space. The usual nonparametric estimator of a linear functional of the stationary distribution is the empirical estimator. If the stationary distribution obeys finitely many known linear constraints, we can improve the empirical estimator by empirical likelihood weights. Since the observations are dependent, an optimal choice of weights is determined by weighting averages over disjoint blocks of observations with slowly increasing length. We show that the improved empirical estimator is efficient. We also introduce two additively corrected empirical estimators that are asymptotically equivalent to the weighted empirical estimator, hence also efficient.