Which are the most developed majority non-white countries?

[Middle-aged Europe]

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

[Middle-aged Europe]

Different cases. Chile is Mestizo majority, so non-white. Argentina is "whiter" than the US and NZ.

Chile is definitely debatable, because I found very conflicting numbers on this. According to a survey from 2011, 59% of all Chileans define themselves as "white", 25% as "mestizo" and 8% as "indigenous". Since human "races" mostly exist as a social construct, one could argue that you're white as soon as you claim you're white.

A genetic study from 1994 also stated: "At present the Chilean population is approximately 64% white and 35% Amerindian with traces of other admixture." (http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1050080/pdf/jmedgene00288-0042.pdf)