You seem to have neglected to tell us what you are trying to do!
I have been trying to figure this out for two days but I don't seem to be reaching a conclusion
Let me describe what I'm doing...
I have a vector of constants:
I obtain a vector of random values, by adding a vector of AGWN, , to :
Finally, I compute between and :
As you can see, the value of would change each time I generate a new vector of AWGN noise. Therefore I will average over several trials.
What I can't get my head round is how can I decide how many trials are enough?
I have gone on various errands to standard error of the mean, confidence intervals, and Monte Carlo trials, without fruition.
Your input is appreciated!
Oh yes...here goes
I want to obtain an accurate value of . I know that sounds very vague - what do I mean by "accurate"?...
Well, I could go on taking averages of ad infinitum to get a better and better estimate of . This isn't practical, and also I can't just decide to take 10 000 averages because it looks big enough.
What I must do is determine how many averages of give a 'good' representation of the r.v. .
My knowns are:
A vector of constants
is white noise of
and is defined as . The value of will fluctuate as (white noise) is different each trial.
I hope my description hasn't obscured things, it is a simple concept I'm sure. Please tell me if anything needs any clarification.
Let me try and sum it up very simply:
All vectors have the same length.
(vector of known constants) (known variance and mean)
(i.e. the correlation coefficient between and ).
My objective: Repeat Steps 1 and 2 times to obtain a simple average of . The question: what approaches can I take for deciding ?