We saw it Friday night. Great flick.
Spoilers!!!!!
I read an article where the director said he left it open for your own interpretation on how it ends. BS. When His daughter looks out the window, looks up and smiles.....he made it and was flying off. He saved his career, his relationship with his daughter and was now flying off to save the world.
SPOILERS:
The first way I interpreted it is that he actually died after he shot himself on stage, and that the hospital part was just some sort of heaven where he was at peace with literally everything/everybody.
The second way, is that he actually survived and in some way killed the Birdman by shooting his own nose (referring to the beck). However he still have this idea of freedom/happiness. So I concluded that he actually didn't jump out the window but just walked away from the room. The same way he jumped from the building while he actually took a taxi, earlier in the movie. People seemed to be cheering when this happened, which probably came from his imagination. So his daughter smiling of admiration was probably from his imagination too.