I have a function X, and two different approximator functions A and B
(A-X) is Gaussian (or at least appears to be from mean, variance, skew
and kurtosis calculations) with zero mean and variance of Va
(B-X) is Gaussian (or at least appears to be from mean, variance, skew
and kurtosis calculations) with zero mean and variance of Vb
Va is less than Vb, i.e. A tends to give a better estimate of X than B
does.
My question relates to the distribution of A.
I would like to be able to express this in terms of B (and/or its
distribution) and X.
As a first guess I used just the distribution of A and the value of X,
but quickly realised that this doesn't take account of the correlation
between A and B, i.e. if A underestimates X, then more often than not,
B underestimates X also.
My next suggestion would be to used E(B-A) and X. If I generate a
particular value of A (let us call it 'ax') from its distribution
(about X). Average this value with b and add it to E(B-A).
therefore a=[ax+b]/2+E(B-A)
Is this a reasonable thing to do, or is there a better way?
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