- We want to compute functionals \(\theta = T(F)\), e.g.
- the mean: \(T(F) = \int x \, dF(x) = \int x \, f(x) \, dx\)
- the median: \(T(F) = F^{-1}(1/2)\)

- Parameter of interest \(\theta\) is functional of unkown \(F\)
- Assumptions on \(f(x)\) relatively weak, e.g. symmetric around zero
- We tested \(\theta = \theta_0\) from a sample \(\boldsymbol{x} = \{ x_1,x_2,\dots,x_n \}\) drawn from distribution \(F\) by comparing the observed statistic \(s(\boldsymbol{x})\) to the null distribution of test statistics
- We introduced estimators \(\widehat{\theta}\) and confidence intervals from a sample
- We quantified the robustness of estimators \(\widehat{\theta}\) to outliers