Make them PROVE they dropped it off at your house! There are people that follow Fed-x and UPS trucks around, and snatch packages right after they are dropped off. So that's possible. However, they would have had to leave it at your house first. If they can't prove it, make them come up with the insurance, or tell them you are going to sue in small claims court.
Better yet, if you paid via PayPal, file a claim with them. If they can't prove they delivered it with a signed receipt from YOU, PayPal will refund your money.