What is the precise mathematical definition of the positive and negative subscript signs as in the following function?

$f(\mu) = \displaystyle\sum_{i=1}^n \alpha (x_i - \mu)_{+} + (1- \alpha)(x_i - \mu)_{-}$

  • 5
    $\begingroup$ Possibly: $z_+=\max (z,0)$ and $z_ -=\min (z,0)$. Does that make sense in your context? $\endgroup$
    – lulu
    Apr 13, 2016 at 13:49
  • $\begingroup$ 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! $\endgroup$
    – JStrahl
    Jan 25, 2017 at 8:20
  • $\begingroup$ Similar question with further discussion math.stackexchange.com/questions/215211/… $\endgroup$
    – JStrahl
    Jan 25, 2017 at 8:23
  • $\begingroup$ 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. $\endgroup$
    – Dron4K
    Sep 17, 2022 at 13:00


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