The author of the epistle to the Hebrews had previously visited the recipients and intends to travel to them again (Heb 13:19, 23). This suggests that the author was a man, since women rarely, if ever, traveled, except in the company of male members of their households. This point has been overlooked, as far as I can tell.
I argued here that those who travelled among the diaspora churches were all men. I think that women could take any role in the early church, but (due to the misogyny of the wider non-Christian society) did not travel. Most of the New Testament was written by people, such as Luke and Paul, who, through travel, had witnessed events and developed relationships that gave them occasion to write histories and letters. This, I think, goes a long way to explaining why no New Testament document is attributed to a woman. Women, I suggest, had the authority to write scripture, but, since they did not travel, they did not have the occasion to write it.
Tal Ilan's "The Lexicon of Jewish Names in Late Antiquity Part III The Western Diaspora 330BCE-650CE" contains 1230 entries for females and 4419 entries for males. Ilan conveniently gives a description field for each entry, in which she includes any references to the person's place of origin in the source. For example, an epitaph records Judah "of Tarsus" (Ταρσεύς). I laboriously searched all 1230 female entries and found just 18 with a place of origin description. I then searched a representative 1230 male entries and found some 45 such entries. From this we can project that the data base contains about 162 male entries with a place of origin description. By any measure, therefore, far fewer women than men had a place of origin description. This does seem to support the assumption that women rarely travelled. Reference to a person's place of origin is unlikely if the person was born, lived, and died in the same location.
Some have argued that Hebrews was written by Prisca/Priscilla. I am grateful to Ruth Hoppin for making the evidence available here and here, and to Brian Small for hosting some further discussion here and here. I would be interested to know how Ruth and others respond to the evidence that women did not tend to travel on church business.