Testing Proportions for Markov Dependent Bernoulli Trials
研究了正递归马尔可夫依赖伯努利试验中平稳状态分布的检验问题，证明了Tavaré和Altham提出的尺度校正统计量XXTA2的渐近最优性，并给出了有限样本性能的模拟结果。
For testing stationary state distribution of positive recurrent Markov dependent Bernoulli trials, Tavaré & Altham (1983) proposed a scale-corrected statistic, XXTA2 which has a X2 limiting distribution. In this paper, we establish the asymptotic optimality of XXTA2 by showing that it is asymptotically equivalent to the optimal test XXTA2 obtained under the modified likelihood approach of Billingsley (1961). Some simulation results are also given to examine finite sample performance of XXTA2 and XXTA2