How to initialize weights in IRLS?

On the wikipedia page about IRLS it is stated that:

$W^{(t)}$ is the diagonal matrix of weights, usually with all elements set initially to: $w^{(0)}_i = 1$

but without any direct reference to the source of this information. Why is this the "usual" way of initializing the weights? Are there other ways to do it that might offer any advantages?


In the absence of a prior about the weights, it is natural to democratically specify "equal believability to all readings" . If there is evidence of a statistically significant departure from this assumption by finding error variances that demonstrably change over different time periods then we are motivated to alter the weights. I can think of no other way other than in a delphi-type approach obtain prior estimates of these varying degrees of belief..

  • $\begingroup$ It is hard to see how this is pertinent to the question: IRLS is not about degrees of belief, nor will altering the initial weights make much difference in general, because IRLS is a procedure that finds appropriate weights to accomplish a robust regression. $\endgroup$ – whuber Dec 10 '16 at 22:38
  • $\begingroup$ IRLS is all about degrees of belief as it weights(believes) each value , possibly differently. Weighted least squares essentially uses different (weights) to reflect possible heterogeneity in the error variance. $\endgroup$ – IrishStat Dec 10 '16 at 22:59
  • $\begingroup$ Could you provide a reference for that? I have encountered IRLS only in the context of robust regression and smoothing techniques, where "degrees of belief" was never a consideration. $\endgroup$ – whuber Dec 10 '16 at 23:02
  • $\begingroup$ forget the word degree of belief just replace it with weights . docplayer.net/… is a reference for identifying weights (transformations) $\endgroup$ – IrishStat Dec 10 '16 at 23:13
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    $\begingroup$ @IrishStat in view of your concessions what value is there left in your answer? $\endgroup$ – Michael R. Chernick Dec 11 '16 at 0:46

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