Bootstrap multiple tests with variance stabilization: application to optimal sensor location

The author reviews and discusses bootstrap methods for testing parameters in situations where sample size tends to be small or the distribution of the test statistic cannot be derived analytically. A bootstrap based variance stabilizing transformation for the parameter under test is considered. This procedure is crucial if the test is to have good power properties and also for the accuracy of the test level. These techniques are applied for comparing multiple coherences, a test which arises in finding optimal sensor locations for knock detection in spark ignition engines. Simulation and experimental results are presented as obtained on a test bed. The tests proposed are multiple tests and permit the finding of optimal positions for sensor groups to control knock in several cylinders at various rotation speeds.<>