minimum variance of a rational function estimator



I am trying to assess the quality of function estimate, and just
wonder
if I can assume that the variance of a rational function is minimum
if
the coefficient of the rational function is obtained from a minimum
variance estimate.

For example, if f(x) = ( a.x+b.x^2+c.x^3 ) / (d.x+e.x^4)


If a, b, c, d, and e are the mimimum variance coeffient estimates
obtained from estimating of a time serie, Can we conclude that the
f(x) has a minimum estimated variance?

.



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