Have objective and verified tests been done of the effects of personal electronic devices on a commercial airliner's operation?
Yes, they have done a lot of testing, hence why they now finally realize that most electronics are of no harm, and you can use them.

The FAA announcement page has a link to a fact sheet of their report, as well as a link to the PDF of the report.

In addition to the FAA report, other agencies have weighed in (such as Boeing).  Basically, the rules were instituted in the 1960s, and remained virtually unchanged since then, so it was time to make a change.