I'm trying to understand how the Adaptive part of Adaptive Lasso works. I understand that theoretically, the weights for zero coefficients are inflated to infinity. But can someone explain this section from the Zou 2006 paper (https://pages.cs.wisc.edu/shao/stat992/zou2006.pdf)?

"Remark 2. The data-dependent ˆw is the key in Theorem 2. As the sample size grows, the weights for zero-coefficient predictors get inflated (to infinity), whereas the weights for nonzero-coefficient predictors converge to a finite constant. (pg. 1420)"

If I'm not getting this, maybe I don't understand the zero-coefficient concept as well as I think I do. What, in plain English, is the "finite constant" if the weights for each coefficient are supposed to vary?



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