Paramount Pictures referenced Tobe Hooper's Poltergeist in the trailer (a line that's not in final product), which is fitting considering the filmmakers capture a lot of the essence of the Steven Spielberg-produced haunter, only with a fraction of the budget.
After all, think of many of the greatest and most effective ones -- such as "The Exorcist," "Poltergeist," "The Shining," and "The Omen" -- and they all involve children who end up threatened by one sort or another of supernatural entities.
A bit of " Rosemary's Baby " here, " The Shining " there, " Poltergeist " there, not to mention some Japanese stuff, and, of course, "Blair Witch" itself, particularly at the end.