most recent 30 from http://mathoverflow.net 2013-06-20T03:28:30Z http://mathoverflow.net/feeds/question/73015 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/73015/taylor-approximation-of-a-function-of-a-random-variable madison54 2011-08-16T21:36:12Z 2011-08-16T21:36:12Z

<p>Suppose we have a random variable $X$ and a smooth function $g$. We want to calculate the expectation value $\mathbb{E}(g(X))$. To be able to write down at least an approximate solution, we perform a Taylor expansion $g_T$ of $g$ up to second order around the mean of $X$ and use $\mathbb{E}(g_T(X))$ as the approximation.</p> <p>Now, what would be a reasonable estimate of how good this approximation is? Or an estimate that tells me for which $X$ the truncation after second order is justified? </p> <p>Whereas for a real valued function this is clear, in this case I am looking for an adequate statistical dispersion measure. I have simulation data, so can I could actually calculate the measure and then want to make an appropriate approximation to get an analytical insight into my system.</p>