Property sharing condition

A necessary condition for false alarms to disturb the judgment on a given statistics is sharing with the statisticsâ€™ property that we consider

Alarm scaleup nature

If an alarm vector \(S^{0.5}(\mathbf{s}{\tilde{\mathbf{s}}})\) falls within a rejection domain, \(\gamma S^{0.5}(\mathbf{s}{\tilde{\mathbf{s}}})\) will also fall within the rejection domain for any \(\gamma >1\)

Least complexity principle

A rejection domain is modelled by a smallest number of parameters that can be well determined from given samples
