4 ms·
> It is easy to prove that... Reminds me of a similar comment in the margin of a old book: http://en.wikipedia.org/wiki/Fermats_Last_Theorem http://en.wikipedi
by bjornsing 14y ago
> It is easy to prove that...
Reminds me of a similar comment in the margin of a old book: http://en.wikipedia.org/wiki/Fermats_Last_Theorem http://en.wikipedia.org/wiki/Fermats_Last_Theorem. :)
But it does sound both plausible and brilliant. How do you prove it (in broad terms)?
- deleted 14y ago[deleted]
- toemetoch 14y agoIn a normal distribution the probability of a value higher or lower than mean is 50%. So if you find mean, the average of your +1/-1 noise is zero -> if you're on mean you'll remain there. If you're not on mean you have a (50 + error)% chance of moving towards mean and (50 - error)% chance of moving away from mean on the next random value -> the trend is towards mean.
- geebee 14y agoas we said in college, "the proof is trivial and is left for the grader"
- tel 14y agoI can't think of an easy proof but it is clear that such a sequence of estimators, {V_n}, has the median as a fixed point in the following sense. Assume V_(n-1) = median(X) for the data stream X_n. Now we have E[V_n | V_(n-1)] = V_(n-1) + E[signum(V_(n-1) - X_n)] but by the definition of the median, the right hand side expectation is 0, so the random process is fixed in expectation. Proving it'll converge to that value would be harder, though. It'll probably depend on the data being much larger than the step size (which is 1).
- derleth 14y agotoemetoch, who is dead, said: "In a normal distribution the probability of a value higher or lower than mean is 50%. So if you find mean, the average of your +1/-1 noise is zero -> if you're on mean you'll remain there. If you're not on mean you have a (50 + error)% chance of moving towards mean and (50 - error)% chance of moving away from mean on the next random value -> the trend is towards mean."
- toemetoch 14y agotoemetoch, who is dead ... I'm not following. I can see my reply a few posts down. I accidentally hit submit twice, deleted one but the second one is still there. Edit: The same technique can be found in some 1-bit ADCs, I believe it's delta-sigma ADC.
- deleted 14y ago[deleted]
- derleth 14y agoOdd. I still only see one response from you with that content, and it is dead.
- njs12345 14y agoSlightly off topic, but looks like toemetoch has tripped one of the hellban filters, isn't a spammer, and has no contact info in his profile. Might want to sort that out if you're reading this toemetoch!