Approximations for two-dimensional discrete scan statistics in some block-factor type dependent models

We consider the two-dimensional discrete scan statistic generated by a block-factor type model. Under the null hypothesis, in which the block-factor model is obtained from an i.i.d. sequence of random variables, we present an approximation for the distribution of the scan statistics and the corresponding error bounds. Numerical results are presented to evaluate the accuracy of the approximation discussed in this paper.