Thread: How many averages are enough?

Hi,

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!

Thanks.

You seem to have neglected to tell us what you are trying to do!

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.

Thanks.

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 ?

Thanks.