At dinner, I spoke to Peter Higgs and said that I hope he wasn't offended by my statement - he wasn't. Then he said, "You're from Brookhaven, right. Make sure to tell Sid Kahana that he was right about the top quark 175 GeV and the Higgs boson 125 GeV".
--M.J.Tannenbaum, "Waiting for the W and the Higgs", arXiv:1608.06934
In 2009, Shaposhnikov and Wetterich successfully predicted the Higgs boson mass, by assuming that quantum gravity is asymptotically safe. Asymptotic safety remains a minority research program, but the paper itself is now well-known among people studying the metastability of the electroweak vacuum, with over 100 citations.
However, there was a paper which in 1993, predicted the Higgs mass and the top quark mass, and which remains almost unknown - though it was known to Peter Higgs himself, as the quote above reveals.
I'd say there are three relevant papers.
D.E. Kahana, S.H. Kahana. "Standard Model Bosons As Composite Particles". Phys.Rev. D43 (1991) 2361-2368. inSPIRE record
D.E. Kahana, S.H. Kahana. "Top and Higgs Masses in Dynamical Symmetry Breaking". Phys.Rev. D52 (1995) 3065-3071. arXiv:hep-ph/9312316
D.E. Kahana, S.H. Kahana. "Higgs and Top Masses from Dynamical Symmetry Breaking - Revisited". arXiv:1112.2794
The 1991 paper (available as a KEK scanned document) introduces the model. The 1993 paper (published in 1995) makes the predictions. The 2011 paper revisits the predictions on the eve of the official Higgs discovery.
The model itself is based on the well-known NJL model of Nambu and Jona-Lasinio. The NJL model is an ancestor of the standard model's electroweak+Higgs sectors, and it's also an approximation to the low-energy scalar sector of QCD (i.e. pions and sigma meson), and it is still studied in many forms.
Kahana and Kahana modify it in an unusual way. The NJL model has emergent scalars and pseudoscalars. Kahana and Kahana add vector interactions in order to produce the electroweak gauge bosons as bound states.
They do a few other things that seem a little strange, too. But in the end they get the Higgs boson mass, the top quark mass, and even the weak mixing angle. And it's a renormalization group argument, as is that used by Shaposhnikov and Wetterich. There may even be some relationship.
This forum contains a number of fans of the prediction from asymptotic safety (I am one of them); I think we should also want to understand how this other, earlier, broader prediction works too.