I'm reading ESE (Element of Statistical Learning) and i'm struggling with this part: 1
My questions are:
- why $ε$ is proportional to $ N(0,σ^2) $ ?
- can you explain the second part of the text underlined in red? in particular, what is $l_i(x_0)$ and why it has been introduced?
Ty very much guys!
It doesn't say that $\varepsilon_i$ is proportional to $\operatorname N(0,\sigma^2);$ rather it says that the probability distribution of $\varepsilon_i$ is $\operatorname N(0,\sigma^2).$ Thus the probability density function is a "bell-shaped" curve centered at $0,$ and the standard deviation, which is the distance from $0$ to either of the two inflection points of the curve, is $\sigma>0.$