Construction of conservative test for change-point problem in two-dimensional random fields

This paper is concerned with a change-point problem in random fields. Tests for detecting a change-structure in a two-way table are constructed. Solutions to this problem require calculations of multiple integrals, but the calculations become difficult as the table gets large. To overcome this difficulty, the tube method is developed in differential geometry. It is shown by simulations that the proposed method is superior to other available methods.