 Variance bound for a weakly self-bounding function

ID: variance-bound-for-a-weakly-self-bounding-function

Z = f (X_{1}, \dots, X_{n})

of independent random variables, the coordinatewise variance inequality gives

Var (Z) \leq E \sum_{i} (Z - Z_{i})^{2} \leq E Z,

where

Z_{i} = f_{i} (X^{(i)})

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