Table 1 Construction principles and the corresponding treatment selection rules
Construction principle | Treatment selection rule |
|---|---|
estimator (EST) | \(\mathcal {C}_{\text {EST}} := \{ x \mid \hat \theta (x) \geq 0 \}\) |
95 percent pointwise confidence band (POI) | \(\mathcal {C}_{\text {POI}} := \{ x \mid l_{p}(x) \geq 0 \}\) |
95 percent simultaneous confidence band (SIM) | \(\mathcal {C}_{\text {SIM}} := \{ x \mid l_{s}(x) \geq 0 \}\) |
95 percent confidence interval of all roots (CIR) | \(\mathcal {C}_{\text {CIR}} := \{ x \mid \hat \theta (x) \geq 0 \} \ \backslash \bigcup \limits _{x_{r} \in \theta ^{-1}(0)} \text {CI}(x_{r})\) |