Psycho

Carpenter put the debt on screen rather than in an interview, three times over:

• The psychiatrist is called Sam Loomis, the name of Marion Crane's lover in Psycho
• Laurie Strode is played by Jamie Lee Curtis, Janet Leigh's daughter, cast for exactly that reason
• The film opens inside the killer's eyeline and holds it there, extending the identification Psycho made possible in 1960

Psycho is the reason a mainstream audience would sit with a murderer at all. Halloween is what the genre built on top of that permission.

Both killers are built on the Ed Gein case, and Jonathan Demme has spoken about the Hitchcock debt rather than deflecting it. The structural inheritance is the more interesting half: Psycho made the audience's sympathy for a murderer the point of the film, which is the position Hannibal Lecter occupies for the next thirty years of the genre. https://en.wikipedia.org/wiki/Ed_Gein