Talk:Rademacher distribution

From Wikipedia, the free encyclopedia
Jump to: navigation, search
WikiProject Mathematics (Rated Start-class, Low-importance)
WikiProject Mathematics
This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of Mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
Mathematics rating:
Start Class
Low Importance
 Field: Probability and statistics
WikiProject Statistics (Rated Start-class, Mid-importance)
WikiProject icon

This article is within the scope of the WikiProject Statistics, a collaborative effort to improve the coverage of statistics on Wikipedia. If you would like to participate, please visit the project page or join the discussion.

Start-Class article Start  This article has been rated as Start-Class on the quality scale.
 Mid  This article has been rated as Mid-importance on the importance scale.
 

Unclear section on bounds[edit]

A section added today entitled Bounds on sums says

Let x be a random variable with a Rademacher distribution. Let yi be a sequence of real numbers. Then
  P( \sum ( x y_i ) > t || y ||_2 ) \le e^{ \frac{ t^2 }{ 2 } }


where || ||2 is the quadratic norm and P(a) is the probability of event a.

I have various problems with this. First, on Wikipedia we denote random variables with capital letters (X instead of x). Second, t needs to be defined and given a range. Third, the summation is unclear: is the random variable X taking on various values xi (in which case it should be xi in the summation) so that we are simply taking a weighted sum of independently drawn values of X? Or is it something else? This needs to be clarified. Fourth, this inequality says that a probability is less than or equal to something that is always greater than 1, which is always true of probabilities and so provides no information about this particular distribution. Fifth, y is not defined -- is it supposed to be the vector with elements yi, so that ||y||2 is the square root of the sum of the squares of the yi? Sixth, while the section title mentions bounds on sums, this is apparently intended to be a bound on a probability.

Then the new section says

If ||yi||1 is finite then
 P( \sum ( x y_i ) > t || y ||_1 ) = 0

The same questions apply to this, and also the norm ||.||1 needs to be explicitly defined.

Given that the new section is currently uninterpretable, I'm reverting it. I hope that it will be substantially clarified and reinserted. Duoduoduo (talk) 16:54, 14 May 2013 (UTC)