Rasmusen p1vaim at 16:40, 25 May 2021

2021-05-25T16:40:15Z

Rasmusen p1vaim: 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 $..."

2021-05-25T16:39:27Z

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 $..."

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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.

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- 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.
+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.
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Outliers - Revision history

Rasmusen p1vaim at 16:40, 25 May 2021

Rasmusen p1vaim: 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 $..."