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I have to mention GAM (generalized additive models), MARS (multivariate adaptive regression splines), and LOESS in an academic paper.

I think GAM and MARS are capitalized in most cases, but not sure about LOESS. I saw LOESS, Loess, and loess all.

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LOESS is an acronym of locally weighted scatterplot smoothing and as such is commonly written in uppercase. On another hand, some acronyms are written in lowercase and the rules are not that clear cut, as noticed e.g. in The Economist style guide:

Abbreviations that can be pronounced and are composed of bits of words rather than just initials should be spelt out in upper and lower case: Cocom, Frelimo, Kfor, Legco, Mercosur, Nepad, Renamo, Sfor, Unicef, Unison, Unprofor, Trips (trade-related aspects of intellectual property rights). There is generally no need for more than one initial capital letter, unless the word is a company or a trade name: MiG, ConsGold. (...)

Most upper-case abbreviations take upper-case initial letters when written in full (eg, the LSO is the London Symphony Orchestra), but there are exceptions: CAP but common agricultural policy, EMU but economic and monetary union, GDP but gross domestic product, PSBR but public-sector borrowing requirement, VLSI but very large-scale integration.

See also https://english.stackexchange.com/questions/51924/proper-capitalization-of-commonly-used-acronyms

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    $\begingroup$ LOESS being an acronym of locally weighted scatterplot smoothing may not be correct. Based on this discussion, LOESS actually stands for "local regression models". $\endgroup$ – burger Mar 29 '19 at 5:23

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