What is the precise mathematical definition of the positive and negative subscript signs as in the following function?
$f(\mu) = \displaystyle\sum_{i=1}^n \alpha (x_i - \mu)_{+} + (1- \alpha)(x_i - \mu)_{-}$
Asked
Active
Viewed 7,130 times
3
-
5Possibly: $z_+=\max (z,0)$ and $z_ -=\min (z,0)$. Does that make sense in your context? – lulu Apr 13 '16 at 13:49
-
Do you have a reference to the source of this function? Typically any text with mathematics should have a notation section that should have what you are looking for. In my experience there are different notations for mathematicians, physicists, computer scientists, engineers and more! – JStrahl Jan 25 '17 at 08:20
-
Similar question with further discussion http://math.stackexchange.com/questions/215211/meaning-of-mathematical-operator-that-consists-of-square-brackets-with-a-plus-si – JStrahl Jan 25 '17 at 08:23
-
For example if you open The Elements of Statistical Learning by Hastie, etc. Second Edition. p.71. Table 3.4. Here the author explains x with + subscript as positive part of x, where x is a function. I think it is analogically for minus. Looks like it depends on context. I was also wondering what that notation means. – Dron4K Sep 17 '22 at 13:00