398 PART TWO: RELAXING THE ASSUMPTIONS OF THE CLASSICAL MODEL
population regression function (PRF) more reliably we would like to give more weight to observations that are closely clustered around their (population) mean than to those that are widely scattered about.
Since (11.3.11) minimizes a weighted RSS, it is appropriately known as weighted least squares (WLS), and the estimators thus obtained and given in (11.3.8) and (11.3.9) are known as WLS estimators. But WLS is just a special case of the more general estimating technique, GLS. In the context of heteroscedasticity, one can treat the two terms WLS and GLS interchangeably. In later chapters we will come across other special cases of GLS.
In passing, note that if wi = w, a constant for all i, ¡¡2 is identical with ¡2 and var (¡2) is identical with the usual (i.e., homoscedastic) var(32) given in (11.2.3), which should not be surprising. (Why?) (See exercise 11.8.)
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