2016-09-05(Chap1a).pdf

# 2016-09-05(Chap1a).pdf - Parameter RISK function R,d...

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RISK function, R( θ ,d) Parameter, θ Action, a Observed data, x Decision rule, d( x ) = a

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RISK function, R( θ ,d) Parameter, θ Action, a Observed data, x Decision rule, d( x ) = a
draw 1 at random 10 batteries Test it 𝑿𝑿 = 𝟎𝟎 𝑿𝑿 = 𝟏𝟏 good bad

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𝜽𝜽 Consider 4 risk functions: 1 2 3 4 1 2 worse than 3 BUT 3 4 No clear winner
strictly dominates 𝜽𝜽 Consider 4 risk functions: 1 2 3 4 Terminology: 3 1 2 admissible 3 4 strictly dominated by no other rule not inadmissible

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Formal definitions: strictly dominated by no other rule In practice, consider only admissible rules (discard inadmissible rules out of hand). This is a minimum requirement. Still, there may remain a large set of admissible rules for consideration

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