MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I'm looking at some statistical literature and trying to compare the results given there in probabilistic big-Oh notation with statements I'm more familiar with.

In particular, I'm trying to interpret statements of the form $$ \|\Sigma_{n(p)} - \Sigma \| = O_P\left( \frac{\log p}{n(p)}\right). $$ As far as i can tell from the rather terse wikipedia page on $o_p$ notation, this means that there is some constant $C$ that is independent of $p$ for which $$ \lim_{p \rightarrow \infty} \mathbb{P}\left( \|\Sigma_{n(p)} - \Sigma \| > C \frac{\log p}{n(p)}\right) = 0. $$

Is that correct?

share|cite|improve this question
up vote 1 down vote accepted

The problem is that there are no universally agreed upon notations. Maybe this will help.

share|cite|improve this answer
Thanks for the reference. I think I'll also work through a couple of the proofs because I'm interested to see whether they prove their results by getting explicit tail bounds that hold for finite p (and then just state the theorem in a weaker way because of convention) or by using arguments that only hold asymptotically. – Alex Gittens Nov 3 '11 at 14:19

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.