|WikiProject Mathematics||(Rated Start-class, Low-importance)|
|WikiProject Statistics||(Rated Start-class, Mid-importance)|
Unclear section on bounds
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
- 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
The same questions apply to this, and also the norm ||.||1 needs to be explicitly defined.