Is there any difference between the two terms "Least Squares Estimator" and "Ordinary Least Squares Estimator". For convenience, I'll refer to them as LS and OLS respectively. I have read various articles on this and could find LS, OLS, Weighted LS, Fuzzy LS and so on. But my problem is between LS and OLS. Are they referred to the same method of estimation or not?

https://cpb-us-w2.wpmucdn.com/people.uwm.edu/dist/2/109/files/2016/04/2000_NAAJ-zdngkl.pdf

Please see page 9/22 of the above link for reference.

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#### Best Answer

Dropping out the *Estimator* keyword, *Least Squares* and *Ordinary Least Squares*, referred as *LS* and *OLS* respectively, are not the same. LS is much more general. It consist of linear and non-linear LS. And, linear LS consist of OLS, and some other types (e.g. GLS: Generalized LS, WLS: Weighted LS). The nonlinear part is itself a different world. In LS methods, the key thing is minimizing the sum of squared residuals. So, any one of the above listed method having this objective functions is a LS estimator. So, LS estimator is not that much definitive. When you make assumptions about the model and the error, it'll boil down to some of the listed alternatives. But, sometimes (and maybe commonly), it is being used for referring to OLS. The author of any article/note saying just LS estimator is probably referring to some sort of special case of it, by making related assumptions, probably somewhere in the article/notes. In your link, Page 9, Section 4.4, it is referring to OLS, in which he actually refers to it in the beginning of the second paragraph.