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By some googling it seems like there exist some kind of expansion of the Taylor series for statistical functionals. I can however, not sort out how it is working and what the derivative-equivalent of the functional actually is.

My situation is that I have a functional, say \theta which depend on the distribution function given to it. I want to expand \theta(f_1 + f_2) around the distribution function f_1. I think it should look like

\theta(f_1(y) + f_2(y)) = \theta(f_1(y)) + \frac{d \theta}{d (something)} *f_2(y) + o(1),

but I do not know what the derivative-equivalent actually is.

What is the definition of this and how can it be calculated in a given situation? Or am I totally out of bounds with such a formula?

Can someone help me or at least point me in the right direction?

Any help is appreciated.

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# Expansion of Taylor series for statistical functionals

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