1. The camera is very far away, and during the jump we do not get to see the face of the performer.
This is an important factor since it was Jackie's policy to show his face in the same cut as the stunt performance. He showed his face in Project A after the fall, and he showed his face before the stunt in Police Story.Also, it was clear that Jackie was falling into the burning coals in Drunken Master 2.
Some people have said that we first see Jackie running off the car so that proves that he is jumping, but I doubt that since the two different cuts do not go together. When he jumps off the car, as we can see in the picture on the right, he jumps off the car with his left leg first going into the air, and then he swings his left leg back and then to front again, and that makes the end of this shot. But when we see the jump from side ways in the next several shots, we do not see the person swinging his left leg so much. These two cuts simply don't go together. It's been edited.

Counterargument:
But you could say something like - It was impossible to locate a camera near the buildings so they had to shoot from a distance.Yes, very possible.

2. To add to this, the cut in the outtakes where we see Jackie wiggling his butt on the balcony, doesn't seem to go together either.
This is just a guess but, if we watch both the shots where he is jumping, and where he pops out of the building he landed on, it seems like the amount of sunshine is different.  As in the pic on the right, the sun seems to have gone away, leaving less sunlight on the second building. If Jackie popped out onto the balcony soon after he finished filming the stunt, wouldn't there be more sunlight?

Counterargument:
But I can never tell how the clouds will move. Maybe a large cloud was just approaching and covered the sun soon after the stunt finished. Jackie with his 'butt shake' simply proves that he is happy after finishing the stunt.

3. Even outtakes do not prove much, since they made up an outtake in Project A2 for example.
Yes, in the Project A2 outtakes, there is a scene in which the hatchet Chan throws towards the camera actually hits it. Then right after this outtake shot, we then see the cameraman reacting to this and cover his eye as the hatchet hits the camera. This looked pretty much like a fake outtake, unless the crew were totally aware that the hatchet could hit the camera, and were shooting the main cameraman with a different camera from a different position. Possible. But I doubt it. I think it was a deliberate fake shot put in for another bit of entertainment. 

Counterargument:
But well, what is the point in making fake outtakes then? Wouldn't that be considered as deceiving? And after all, the hatchet outtake might not have been a fake one.

1. Jackie says himself that he was the one who is jumping.
Yes, pretty simple.

Counterargument:
But can you actually trust 100% what a person you don't really know in real life says? I mean, have you met the man and talked about this in person? Jackie is an entertainer and a movie maker, right? He is in a position where he sometimes has to tell lies.(Don't tell me that he is not the sort of person that would lie. That's bollocks. How can you be so sure?)

2. To the contrary to what I said in A-2, I think there is a mattress around Jackie's feet when he pops out of the balcony. This mattress was also there when the stunt actually took place. Looking at some of the shots of the jump, I think I can see the floor of the landing point bouncing up a little bit, which I suspect was a mattress for safety. And if this mattress is still there when Jackie pops out, then I think it means that he popped out pretty soon after the jump took place, implying that there isn't much progress in time. Thinking this way, I can easily deny what I've just said about the sunlight.

Counterargument:
Maybe there was no mattress. It is very vague and can't really tell.

3. Maybe Stanley Tong did the stunt as well, but Jackie also did it.
I don't have anything to say to this. Some people claim that they both did it, but used Stanley's jump in the movie simply because it looked better. Or you could even say, they both did it, and that's why people say " Stanley Tong did the jump, but what we see in the movie is done by Jackie. "

Counterargument:
If Jackie had jumped as well, then why didn't they show it in the outtakes? It would be natural for Jackie to at least show his own jump as well counting on his previous ways of showing the outtakes. And okay, even if they both jumped and had decided to use Jackie's jump in the movie, can you really say that was Jackie jumping? The camera is too far away to concentrate on faces, hairstyle, body size, etc...and isn't it very very hard to tell? What makes you so sure?

4. And after all, we do get to see someone who is very much likely to be Jackie Chan showing out of the building and wiggling his butt.
This person looks like Jackie Chan, and I'm pretty sure it is. And so if he comes out onto the balcony to win the applause from the other crew, it has to be nobody else but Jackie Chan.

Counterargument:
Nothing to say really.That guy shaking the butt seems like the man we know as Jackie Chan. True.