Serial dependence in multidimensional contingency tables

Abstract

It is well-known that the Pearson goodness-of-fit test statistic in multinominal trials is asymptotically distributed as $X^2$ with the appropriate number of degrees of freedom. In this thesis, the asymptotic behaviour of the Pearson $X^2$ statistic in multi-dimensional contingency tables which are generated by two or more Markov chains is examined. The explicit results for the effects of such serial dependence on standard test statistic are given and approximately coincide with some results of computer simulation in simple cases.