D.A.V.E. Statue is part of the decoration given to players who subscribed to the monthly D.A.V.E. Club, to signify that you have subscribed to it.
Glitch/Bug with Statue
It has been shown and i have tested it repeatedly that if you subscribe to the D.A.V.E. Club you get the statue and you can actually get multiples. You need the Map Room. First place your DAVE statue on your yard and reload your base by either entering the map or reloading the page. Once that is done your DAVE statue will still be on your yard. Finally enter the Map Room and you will be able to take another statue out of storage. I've contacted the devs and they just said "Thanks, but we can't remove extra statues." so go crazy with your imagination!