Here's a blog article by Razib Khan on a recent paper about the origins of the Japanese. And a link to the article itself.

Basically, the authors sampled Japanese people, northern Chinese people from Beijing and Ainu. They examined whether the Japanese populations could possibly be a mixture of the former and latter populations with the Chinese representing the Yayoi agriculturalists and the Ainu representing the Jomon hunter-gatherers and came to the conclusion that they could. So, going backwards, if using the Ainu as a Jomon-substitute and northern Chinese as a Yayoi substitute results in an admixed population that resembles the Japanese, then the Jomon were related to the Ainu.

But then, even if the paper's assumptions are valid e.g. the Ainu aren't so heavily admixed with the Japanese to bias the results, then you've still got the issue that we have no idea what languages the Jomon people spoke. They're a Pleistocene hunter-gatherer population that had been in place for so long, undoubtedly their languages had diverged, possibly so much to the point they wouldn't even appear related on the surface - consider that the Native American languages are broken up in numerous families despite there only being genetic evidence of 3 migrations from Northeast Asia into North America.

probably better to ask on /r/askanthropology

Here's a genetic study that shows their relations to various groups in asia:http://www.ncbi.nlm.nih.gov/pubmed/14997363