ABSTRACT
Of course, this method will only work in the absence of noise. By this time, I will be disappointed with the reader who fails to see the flaw in this method of estimating f (y) . The problem, of course, is that, when ?i is small, any noise present in the estimate of ai will be divided by a small number ?i. To quantify this, we have to
consider the effect of noise on . Let n(x) be a random variable that represents the noise in the measurement of g(x) . We are really estimating ai from
where ?i is a random variable defined by
The variance of is (remember that its mean value is zero) is
where
Since n(x) is a random variable,
Therefore, if we use equation (68) to invert equation (1), we will find that the
variance of will be
