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- Stein's Lemma:
- E[ g(x) * (x-μ) ] = E[ g'(x) ]
- where g(x) is an everywhere differentiable function of x, and
μ is a location parameter (--Daniel).
-
- If h is a "smooth" function of x, and
E[X]=μ & variance[X]=ν, the expectation
- E[ h(x) ]
- = E[ h(μ)
+ (x-μ) . h'(μ)
+ (x-μ)2/2 . h''(μ)
+ ... ]
--by Taylor expansion
about μ
- = h(μ) + (ν/2)h''(μ) + ...
- which may come in useful for
approximating Fisher information,
etc. (--DS).
-
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