It's been proven time and time again in studies (some are linked in these threads here).I see that claim a lot, but when I look at the "studies" being cited, they rarely stand up to even cursory scrutiny about their methodology and the choice of test subjects.
These studies (or those making a case for TDD based on them) tend to do things like generalising results based on a few undergraduate students writing toy programs to draw conclusions about professional software developers working on industrial-scale applications, or using no unit testing at all as a control rather than say doing either test-first or test-last unit testing but not following the TDD process.
If you have better sources, please do share them. Developing a non-trivial application using two different techniques is rarely cost-effective, even without controlling for having different developers or experience in the two cases, so getting good quality data about the effectiveness of software engineering processes is hard.