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 (Shake)

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.

Re: How many averages are enough?

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

Re: How many averages are enough?

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.

Re: How many averages are enough?

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.