According to the UN's Human Development Index, the "majority non-white" (I'll translate it as non-European descent) countries with a "very high development" are:
12. Japan
13. Hong Kong
15. South Korea
26. Singapore
30. United Arab Emirates
33. Brunei
37. Qatar
42. Bahrain
47. Barbados
Chile and Argentina are also in the "very high development" category, but under my definition their populations are in fact "majority white".
http://en.wikipedia.org/wiki/List_of_countries_by_Human_Development_Index
Different cases. Chile is Mestizo majority, so non-white. Argentina is "whiter" than the US and NZ.