Comments on: How Close Is The Normal Distribution? http://normaldeviate.wordpress.com/2013/02/04/how-close-is-the-normal-distribution/ Thoughts on Statistics and Machine Learning Thu, 23 May 2013 03:05:24 +0000 hourly 1 http://wordpress.com/ By: kindle fire 7 lcd display wi-fi 8 GB includes special offers http://normaldeviate.wordpress.com/2013/02/04/how-close-is-the-normal-distribution/comment-page-1/#comment-7417 Tue, 26 Feb 2013 09:53:13 +0000 http://normaldeviate.wordpress.com/?p=361#comment-7417 [...] Source URL: http://normaldeviate.wordpress.com/2013/02/04/how-close-is-the-normal-distribution/ [...]

]]> By: Csaba Szepesvari http://normaldeviate.wordpress.com/2013/02/04/how-close-is-the-normal-distribution/comment-page-1/#comment-7235 Sun, 17 Feb 2013 05:32:12 +0000 http://normaldeviate.wordpress.com/?p=361#comment-7235 Interesting read, thanks for the pointer!
So the conclusion, with an analogy from the paper, is: “In the United States many consumers are entranced by the magic of the new iPhone, even though they can only use it with the AT&T system, a system noted for spotty coverage—even no receivable signal at all under some conditions. But the magic available when it does work overwhelms the very real shortcomings.” So classical results are like iPhone.
I can understand this:) But then, again, I own an Android phone and tablet;)

]]> By: Comunidades tribais são mais violentas? O quão próxima é a distribuição normal? O papel do BNDES. | Análise Real http://normaldeviate.wordpress.com/2013/02/04/how-close-is-the-normal-distribution/comment-page-1/#comment-7061 Tue, 05 Feb 2013 01:14:46 +0000 http://normaldeviate.wordpress.com/?p=361#comment-7061 [...] Sobre teoremas de upper-bound para erros de aproximação pela curva normal (vale conferir uma sugestão que surgiu nos comentários do post, um texto histórico, bacana, [...]

]]> By: Keith O'Rourke http://normaldeviate.wordpress.com/2013/02/04/how-close-is-the-normal-distribution/comment-page-1/#comment-7044 Mon, 04 Feb 2013 17:11:53 +0000 http://normaldeviate.wordpress.com/?p=361#comment-7044 Csaba:

You might find this paper of interest – Stigler, Stephen M. “The changing history of robustness.” The American Statistician 64.4 (2010): 277-281.

https://files.nyu.edu/ts43/public/research/.svn/text-base/Stigler.pdf.svn-base

]]> By: normaldeviate http://normaldeviate.wordpress.com/2013/02/04/how-close-is-the-normal-distribution/comment-page-1/#comment-7043 Mon, 04 Feb 2013 16:57:26 +0000 http://normaldeviate.wordpress.com/?p=361#comment-7043 I prefer finite sample intervals.
The problem is that there are many, many, many, practical problems where there aren’t
any known finite sample intervals and we are forced to use Normal approximations.
It’s by necessity not preference.
LW

]]> By: Csaba Szepesvari http://normaldeviate.wordpress.com/2013/02/04/how-close-is-the-normal-distribution/comment-page-1/#comment-7037 Mon, 04 Feb 2013 15:22:06 +0000 http://normaldeviate.wordpress.com/?p=361#comment-7037 What still surprises me about statistics or the way statisticians do their business is the following: The Berry-Esseen theorem says that a confidence interval chosen based on the CLT is possibly shorter by a good amount of $c/\sqrt{n}$. Despite this, statisticians keep telling me that they prefer their “shorter” CLT-based confidence intervals to ones derived by using finite-sample tail inequalities that we, “machine learning people prefer” (lies vs. honesty?). I could never understood the logic behind this reasoning and I am wondering if I am missing something. One possible answer is that the Berry-Esseen result could be oftentimes loose. Indeed, if the summands are normally distributed, the difference will be zero. Thus, an interesting question is the study of the behavior of the worst-case deviation under assumptions (or: for what class of distributions is the Berry-Esseen result tight?). It would be interesting to read about this, or in general, why statisticians prefer to possibly make big mistakes to saying “I don’t know” more often.

]]>