In some books both WLS and ADF are considered different methods. In other books, they acknowledge that ADF = WLS, so they are used interchangeably throughout the book.

How solve this confusion?

  • $\begingroup$ WLS = Weighted Least Squares and am I correct in assuming ADF = Asymptotic Distribution-Free Technique? Do you have a reference for where they are considered the same? $\endgroup$ Sep 5, 2020 at 5:50
  • 2
    $\begingroup$ @TyrelStokes ADF is a specific type of WLS so I can understand the confusion. $\endgroup$ Sep 5, 2020 at 7:26

1 Answer 1


Weighted Least Squares (WLS) is a general class of estimators where squared differences between observed and estimated values are weighted by some critereon. When the weights are all 1, this is Ordinary Least Squares. When the weights are based on unequal variances, this is Generalised Least Squares (GLS). For a specific choice of weights, based on the covariance of the disturbance terms, and under conditions where the 4th and 8th moments around the mean of the observed variables exist, but without any other distributional assumptions, this estimator is called the arbitrary distribution function estimator (ADF). It is also sometimes know as the asymptotic distribution-free estimator due to the need for larger sample sizes than for other estimators.

  • $\begingroup$ @Hussain Does this answer your question ? If so, please consider marking it as the accepted answer. If not, please let us know why $\endgroup$ Sep 29, 2020 at 19:17
  • $\begingroup$ Will you elaborate what it means that "the 4th and 8th moments... exist, but without any other distribution assumptions"? a) When is it not possible to calculate these moments? b) if these assumptions require other assumptions, what are they - that moments 1-3 can also be calculated? ... I will be happy to ask a new question should you prefer. $\endgroup$
    – Johan
    Jun 20, 2023 at 10:14

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