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Newton-Raphson can compute an average

In our article How robust is logistic regression? we pointed out some basic yet deep limitations of the traditional full-step Newton-Raphson or Iteratively Reweighted Least Squares methods of solving logistic regression problems (such as in R‘s standard glm() implementation). In fact in the comments we exhibit a well posed data fitting problem that can not be fit using the traditional methods starting at the traditional (0,0) start point. And we cited an example where the traditional methods fail to compute the average from a non-zero start. The question remained: can we prove the standard methods always compute the average correctly if started at zero? It turns out they can, and the proof isn’t as messy as I anticipated. Continue reading Newton-Raphson can compute an average