Monotonicity of Bayes sequential tests for multidimensional and censored observations

For statistical models admitting a sufficient, transitive sequence of one-dimensional statistics, Brown, Cohen and Strawderman proved in 1979 that, under simple conditions verified in many examples, all Bayes sequential tests are monotone. We extend the definition of monotone test to higher dimension in a suitable way, and show that the same result holds for multidimensional statistics. Our work was partly motivated by the observation that deterministically censored observations from a statistical model admitting a sufficient, transitive sequence of m-dimensional statistics can be viewed as observations from another statistical model, still admitting a sufficient, transitive sequence of statistics, but with values in a higher-dimensional space. A typical application to a reliability problem is also discussed.