Detecting Change Points in Sampling from Multinomial Distributions

摘要

The question of if and when a change in the underlying cell frequencies has occurred during the observation of a sequence of categorical variables is analyzed. Several techniques are developed that may be loosely grouped into three classifications: (i) Central Limit Theorem approaches, (ii) Departure from Centrality approaches and (iii) Test of Homogeneity approaches. The approaches monitor the sequence either at every trail or at every k-th trial. All approaches construct statistics which are functions of sequential sums either weighted or unweighted. The behavior of these sums and the statistics developed from them are discussed in detail. A large scale simulation study is discussed in an attempt to assess the performance of the approaches. Three approaches emerge as most promising but a clear choice among these is not possible at present. (Author)