Outliers
Revision as of 09:39, 25 May 2021 by Rasmusen p1vaim (talk | contribs) (Created page with " Suppose you have two observations, $y_1 =70$ and $y_2 = 100$, where $y_i = \mu + \epsilon$ with which to estimate the value of $\mu$, with $\epsilon_1 \tilde N(0,10)$ and $...")
Suppose you have two observations, $y_1 =70$ and $y_2 = 100$, where $y_i = \mu + \epsilon$ with which to estimate the value of $\mu$, with $\epsilon_1 \tilde N(0,10)$ and
$\epsilon_2\tilde \{(.5, -40), (.5, +40)\}$. What should our estimate $\hat{\mu}$ be?
This would make a good note. American Mathematical Monthly. Get a loss function-- probably any convex loss function is OK, but start with quadratic. The answer must be something like 104. The point is: don't discard outliers, but think about what htey mean.
