Assessing the Order of Dependence for Partially Exchangeable Binary Data
研究了如何评估部分可交换二元序列中序列依赖的阶数，通过精确条件检验和蒙特卡洛方法比较不同阶数，并推广了似然比检验的渐近卡方分布。
Abstract The problem we consider is how to assess the order of serial dependence within partially exchangeable binary sequences. We obtain exact conditional tests comparing any two orders by finding the conditional distribution of data given certain transition counts. These tests are facilitated with a new Monte Carlo scheme. Asymptotic tests are also discussed. In particular, we show that the likelihood ratio tests have an asymptotic chi-squared distribution, thus generalizing the results of Billingsley for the particular case of Markov chains. We apply these methods to several datasets, and perform a simulation to study their properties. Key Words: Conditional simulationMarkov chainsModel selectionMultiple binary sequencesNonparametric mixtures