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Math Help - How many averages are enough?

  1. #1
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    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: X
    I obtain a vector of random values, Z by adding a vector of AGWN, N, to X: Z=X+N

    Finally, I compute C between X and Y: C=\sigma_{XZ}/\sqrt(\sigma_{X}\sigma_{Z})

    As you can see, the value of C would change each time I generate a new vector of AWGN noise. Therefore I will average C 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.
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  2. #2
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    Re: How many averages are enough?

    You seem to have neglected to tell us what you are trying to do!
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  3. #3
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    Re: How many averages are enough?

    Oh yes...here goes

    I want to obtain an accurate value of C. I know that sounds very vague - what do I mean by "accurate"?...

    Well, I could go on taking averages of C ad infinitum to get a better and better estimate of C. 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 C give a 'good' representation of the r.v. C.

    My knowns are:

    X: A vector of constants

    Z = X + AWGN

    AWGN is white noise of N(\mu, \sigma)

    and C is defined as C = \sigma_{XZ}/\sqrt(\sigma_{X}\sigma_{Z}). The value of C will fluctuate as AWGN (white noise) is different each trial.

    Thanks.
    Last edited by algorithm; October 8th 2012 at 01:12 PM.
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  4. #4
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    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.

    Step 1. Z = X (vector of known constants)  + White Gaussian Noise (known variance and mean)
    Step 2. C = \sigma_{XZ}/\sqrt(\sigma_{X}\sigma_{Z}) (i.e. the correlation coefficient between X and Z).

    My objective: Repeat Steps 1 and 2 N times to obtain a simple average of C. The question: what approaches can I take for deciding N?

    Thanks.
    Last edited by algorithm; October 9th 2012 at 10:04 AM.
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