It is often used to indicate independence, but I've seen it used to mean uncorrelated (which is more natural IMO, but maybe less used). In the case of vectors, as usual, it can also mean literally orthogonal.
I am reading Properties of sample variance, and suddenly this notation comes up with no introductory explanation what it means
(when proving that the sample variance is an unbiased estimator of the population variance)
Then the next chapter said 'the sample mean and the sample variance are independent,
(the Y was supposed to be sample mean, ie with a bar on top, but I couldn't find the way how to place the bar in Latex?)
So my guess is that this sign in statistical inference denotes mutual independence, but I'd like to check.
PS found this in Google
apparently, (linearly) independent is not the same as orthogonal or uncorrelated. So what exactly does that 'perpendicular' sign denotes?
May I ask another - related - question here (not worth a a new thread). From the same proof, to prove that sample variance is an unbiased estimator of the population variance, the author of my study guide uses a 'trick' of splitting the into independent terms (so that's where the question about sign comes from).
It is done as follows:
I hope you can read that - what is the Latex for 'not equal'??
(And after splitting the sample variance original formula into two parts which are independent, he finds the expected value which, after manipulations, is pop'n variance.)
My question is pretty basic - I don't understand the 'splitting' manipulation above, and especially the meaning of the . Is that the sum of all except the ? Then where is the order of the last term of this sum (I mean n-1 at the top)?
It should be fine for undergrad. You'll end up going quite a bit off the subject matter you're studying, though, if you plan on making a real analysis excursion (though most of the material is mandatory for measure-theoretic probability). Depending on your mathematical maturity, the difficulty of it could range from challenging to impossible. Rosenlict is a more accessible alternative (it is also only $10, whereas Rudin is $100+ unless you illegally download it or something), but I dislike the way he approaches some topics. The exercises in Rudin are very good, challenging, and help to train your mind so that you can understand digest the more difficult material in the sequel.