A decision rule δ∗ is a pareto improvement over another rule δ if and only if R(θ,δ)≤R(θ,δ∗) for all θ, and strictly < for at least one.
Small typo, I think you meant to switch the order of the two risk terms. Otherwise we say that a decision rule is a Pareto improvement if it results in more risk/a higher loss score.
Small typo, I think you meant to switch the order of the two risk terms. Otherwise we say that a decision rule is a Pareto improvement if it results in more risk/a higher loss score.
Thanks!