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I agree. For both the MAD and STD, we are trying to reduce information about the "spread" of a distribution to a single number. Any such reduction must lose inf

I agree. For both the MAD and STD, we are trying to reduce information about the "spread" of a distribution to a single number. Any such reduction must lose information, so you should pick whichever quantity is suitable for your needs. E.g., in the article they mention that the Pareto distribution has finite MAD but infinite variance. This is meant to be an argument against using the STD, but actually the infinite variance tells us something really important that the MAD does not: the law of large numbers /does not apply/ for the Pareto distribution! I think the real message should be to avoid blindly applying techniques and tools (especially formal ones) without thinking about why or what they capture.

eanzenberg 10y ago
Bingo bingo bingo. Reducing the spread of a distribution to a single number is correct for very special distributions. Beyond these special distributions you have to do more study, take more measurements, do more simulations to understand what you have underlying your mean or median.
scottlocklin 10y ago
Taleb is exasperating. Pareto-Levy distributions are statistical nihilism the way Taleb talks about them. Data is very often approximately normal. Or can be approximated with something like Student-T. That includes estimators for volatility in stock returns. If you assume your risk profile can be characterized with standard deviation, well, you're an asshole. It also can't be characterized with MAD. Then you have stuff like this: "MAD is more accurate in sample measurements" -what does this even mean?
- Elrac 10y ago
  Thank you for saying this! I'm just a struggling armchair intellectual, but it seems to me like every half year Taleb comes up with something to loudly hand-wring about, something that nobody else gives a damn about because they're not in the attention whoring business.
  - eruditely 10y ago
    No, he's completely legitimate actually. He's just so far ahead of people that they can't tell. There's a good Kahneman quote saying he's top 100 intellectuals. http://realworldrisk.com/ http://realworldrisk.com/ http://realworldrisk.com/clients http://realworldrisk.com/clients https://scholar.google.com/citations?user=64BtMdsAAAAJ&hl=en https://scholar.google.com/citations?user=64BtMdsAAAAJ&hl=en
- jamez1 10y ago
  >Data is very often approximately normal >If you assume your risk profile can be characterized with standard deviation, well, you're an asshole. Did you know that standard deviation can be used to describe a normal distribution? Or did you contradict yourself on purpose?

eanzenberg 10y ago

Bingo bingo bingo. Reducing the spread of a distribution to a single number is correct for very special distributions. Beyond these special distributions you have to do more study, take more measurements, do more simulations to understand what you have underlying your mean or median.

scottlocklin 10y ago

Taleb is exasperating. Pareto-Levy distributions are statistical nihilism the way Taleb talks about them. Data is very often approximately normal. Or can be approximated with something like Student-T. That includes estimators for volatility in stock returns. If you assume your risk profile can be characterized with standard deviation, well, you're an asshole. It also can't be characterized with MAD. Then you have stuff like this: "MAD is more accurate in sample measurements" -what does this even mean?

Elrac 10y ago
Thank you for saying this! I'm just a struggling armchair intellectual, but it seems to me like every half year Taleb comes up with something to loudly hand-wring about, something that nobody else gives a damn about because they're not in the attention whoring business.
- eruditely 10y ago
  No, he's completely legitimate actually. He's just so far ahead of people that they can't tell. There's a good Kahneman quote saying he's top 100 intellectuals. http://realworldrisk.com/ http://realworldrisk.com/ http://realworldrisk.com/clients http://realworldrisk.com/clients https://scholar.google.com/citations?user=64BtMdsAAAAJ&hl=en https://scholar.google.com/citations?user=64BtMdsAAAAJ&hl=en
jamez1 10y ago
>Data is very often approximately normal >If you assume your risk profile can be characterized with standard deviation, well, you're an asshole. Did you know that standard deviation can be used to describe a normal distribution? Or did you contradict yourself on purpose?