dunno if it is offensive,
but I would pick "oriental" after the George Zimmerman question on Form 4473, that is if they had it on there
I think far east = oriental
http://www.census.gov/topics/population/race/about.html
White – A person having origins in any of the original peoples of Europe, the Middle East, or North Africa.
Black or African American – A person having origins in any of the Black racial groups of Africa.
American Indian or Alaska Native – A person having origins in any of the original peoples of North and South America (including Central America) and who maintains tribal affiliation or community attachment.
Asian – A person having origins in any of the original peoples of the Far East, Southeast Asia, or the Indian subcontinent including, for example, Cambodia, China, India, Japan, Korea, Malaysia, Pakistan, the Philippine Islands, Thailand, and Vietnam.
Native Hawaiian or Other Pacific Islander – A person having origins in any of the original peoples of Hawaii, Guam, Samoa, or other Pacific Islands.