Ben Witherington III, Ph.D., Amos Professor of NT for Doctoral Studies at Asbury Theological Seminary and author of multiple books, including What Have They Done with Jesus?: Beyond Strange Theories and Bad History--Why We Can Trust the Bible, has published on his blog a very interesting article entitled The Rhetorical Character of Hebrews. This entry is apparently the text of a lecture he is (or was) scheduled to give at the Society of Biblical Literature lecture.
At the outset, he takes up the question about the authorship of Hebrews. Of course, there have been numerous theories as to who wrote the book (including some that identify the author as the Apostle Paul), but rather than focus on the "who", he focuses on "why" there is no author identified.
It is of course possible that the author is so well known to the audience that there was no need for such an identification here. I would suggest however, that while that may be true, there is another primary reason for the anonymity of this document.
This document, like 1 John is a homily , in fact D.J. Harrington has called it “arguably the greatest Christian sermon ever written down” It does not partake of the qualities of a letter except at the very end of the document (Heb. 13.22-25), and these epistolary features are added because this sermon had to be sent to the audience rather than delivered orally to them by the author. In fact, H. Thyen, after studying all the evidence for early Jewish homilies, has argued that Hebrews is the only completely preserved Jewish homily of the period, but this is overlooking 1 John, and James as well.
Sermon manuscripts, ancient or modern, do not conform to the characteristics of an ancient letter with addressor or addressee expected at the outset. Neither do other rhetorical forms of speaking, and make no mistake this document involves rhetoric of considerable skill. Hebrews then, to use an oxymoron, an oral document, and in fact a particular type of oral document—a homily in the form of a ‘word of exhortation’ as Heb. 13.22 puts it. It is not an accident that this is the very same phrase used to characterize Paul’s sermon in Acts 13.15. Hebrews is not a haphazard discourse but a piece of polished rhetoric which has been variously categorized as either epideictic or deliberative rhetoric or some combination of the two (see below). Here the point that needs to be made is that the document’s authority rests in its contents, not in its author’s claims to apostolic authority and its contents are grounded in the shared values the author and audience already embrace and affirm. To judge from the end of Heb. 13 it is assumed, but not argued for, that this author has some authority over this audience who knows very well who he is, and can anticipate a visit from him and Timothy before long.
The article goes on and gets into a lot of the content of Hebrews and the style of document it is. I highly recommend it.