sufficient statistics

hi all, i was just wondering if somebody could help me with this. i
want to know if there is some known result for the following problem.

let f(x|t) be a parametric probablity density function where the
parameter is t. let T(x) be (minimal) sufficient statictics. now if we
take expectation of T(x) with respect to t, i.e. E[T(x)] is there any
know result for the quantity | T(x)-E[T(x)] |? either upper bound lower

bound or some other relation? thanks


ps: i'm particularly interested in exponential families. if there is no

such result, is it possible to derive such a result for say,
exponential families?

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