Judging by elite college representation
Elite college representation is a poor metric because of legacy admissions, influence of donors, and the reported efforts to limit Asian admissions.
Look at schools with more merit-based admissions (MIT, Caltech, etc.). Asians are overrepresented to a much higher degree.
Source? Judging by elite college representation [1], they're doing at least as well if not better than Asian Americans (which granted, is not limited to just Asian immigrant children).
1. https://news.ycombinator.com/item?id=24166064