The Sumerians are the earliest known civilization in the historic region of southern Mesopotamia. Believed to have lived from c. 4100 – 1750 BCE. This part of the world can get very hot during the year, so some of the statues with few garments would not be out of line with the climate.
In researching Sumerian culture, the images that are presented provide an account of the types of costume they would have worn during that period of time. It appears men wore what looks to be some type of robe maybe that they pulled over their heads – shoulder straps that connected to the back that was lower than the front. Most representations of men appear to wear a costume that is wrapped and tied about the waist.
The Smithsonian has a statue “Rim-Sin Carrying Clay” – this is a statue of the King of that time. He appears to be rounded at the bottom half as if he were wearing what we would call a “skirt”. However, there does not appear to be a costume on his upper half. 
In the book Development of Sumerian Art by Wooley C Leonard, there are a handful of complete statues that definitively separate the male and female. The male continues to wear a costume on the lower half – in a circular shape (as such we would call it a “skirt”) and the women appear to have what appears to be a “strap” of same material as the rest of the costume – it goes around her one shoulder – it most likely connects the front and back parts of the costume.
In much the same way we study existing extant garments from before the 17th Century and thereafter, we can study the art, carvings, and symbols from a long-ago culture/society/people. Studying these items, provides much detail to their lives, and allows us to look in for ourselves. I have included several images below. These I clipped from the book that is referenced.
Leave a thought in the comments. What do you see in the images?