DISPERSION OF THE ERRORS IS NON-CONSTANT AND NOT RELATED TO THE MEAN (CROSS-SECTIONAL DATA)

• Consider a regression : Y(t) = v0*X(t) + e(t) where e has variance W(t)**2 * VAR and a mean of zero and where W is a vector of weights t in length.
  
  
  This is referred to in the statistical literature as weighted regression . It is standard practice for the weights to be known before-hand rather than boot-strapped from estimated errors (residuals).
  
  The residuals from a model may not have constant variance and consequently estimated parameters may be deficient. One form of non-constant variance is treated by the Box-Cox or lambda transformations. However the best set of weights may not be a function of anything and just simply a vector of values. There are cases in which the user has an "a priori" knowledge of the weights. For example consider, the actuarial economist who has data where each reading is based upon "n" samples. Thus a reading with a large "n" is more credible than one with small "n".