In the following, is "yesterday" a modifier for "late" or is "late" a modifier for "yesterday"?
Terry mills was dumped late yesterday while on a trade mission in Japan. (ABC News)
One way to resolve questions of this sort is to delete one term and see if the sentence still means the same thing. Let's look at this in context; here's the transcript of ABC's story:
The Northern Territory's ousted Chief Minister will arrive home today. Terry Mills was dumped late yesterday while on a trade mission in Japan. He's been replaced by Adam Giles who becomes the first indigenous head of government in Australian history. Mr Mills is expected to touch down in Sydney this morning.
Now let's delete yesterday.
Terry Mills was dumped late while on a trade mission in Japan.
This might be taken two ways: that the dumping took place later than expected, or that it took place tardily, too late to satisfy some unexpressed need. There's nothing to suggest that either of these senses is in play here, and in this form the sentence does not inform us when the dismissal took place—which is key to the story.
Terry Mills was dumped yesterday while on a trade mission in Japan.
There's no ambiguity here; and the sentence does tell us when Mr. Mills was dismissed.
So what late does is tell us at what time yesterday this occurred: it is a partitive determiner which modifies yesterday.
However, as FumbleFingers reminds us, the collocation might in another context bear one of the senses in which late is the main term and yesterday served as a modifier; in this case yesterday would be a non-restrictive appositive and would be set off with commas or dashes, and would probably itself be qualified by some such term as only:
Terry Mills was dumped late—only yesterday—while on a trade mission in Japan.