I am saying no-one in year 2004 can accurately claim a blood line to the Ancient Israelites. I brought up Jesus because he was born to a Jewish mother and had brothers and there DNA through there children would not be traceable...
This sad little lizard told me he was a brontosaurus on his mother's side. I did not laugh, people who boast of ancestry often have little else to sustain them. Humoring them costs nothing and adds to happiness in a world in which happiness is always in short supply.
Robert Heinlein
Jesus is a bad example. He is one man. Tracing a genetic link to a single man in the past would require that you have his DNA on hand so you can compare the Y-chromosome and adjust for genetic mutation.
But, trying to determine Jewish ancestry isn't that hard. The goal isn't to say that these genes are Jewish. It is to demonstrate that Jews from another geographic location share certain genetic characteristics with their Middle Eastern brethren. The Israelites are a people, and DNA from the descendants of Israel that never left the Middle East is still available. A comparative genetic analysis shows that European Jews have Middle Eastern links. Iraqi Jews and North African Jews are nearly identical. And Palestinian Jews (before the meaning of Palestinian changed) share genetic similarities with all of these groups.
Jews typically marry within their faith, so regardless of where they are in the world, certain genetic characteristics are going to carry through through all the generations.
That's pretty much what the studies found. Intermingling with other races may have altered their appearances somewhat, but Jews from many places around Asia, Europe, and Africa share enough genetic similarity with the Middle East to indicate ancestry in that region.
When compared to the populations in which they lived, the similarities were deemed statistically significant because the Jewish populations in areas like Germany were dissimilar from their neighbors in those aspects that point to the Middle East ancestry.
You really should read about it.