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What is In a 10 year old female patient of Asian ethnicity, which of the following methods would be the best approach to estimate the  size of unerupted permanent teeth? and explain in detail?
The Moyers, Tanaka-Johnston and Staley-Kerber predictions are all based on data from white school children of northern European descent. If the patient fits this population group, the Staley-Kerber method will give the best prediction, followed by the Tanaka-Johnston and Moyers.
On the other hand, if the patient does not fit the population group, as an African or Asian child would not, direct measurement from the radiographs is the best approach.

Huckaba analysis:
The formula recommended by Huckaba was used in all radiographic measurements: 
X = (y) (x1)/(y1) 
where X is the estimated size of the permanent tooth, x1 is the radiographic size of the permanent teeth, y is the size of the primary mandibular second molar on the cast and y1 is the radiographic size of the primary molar.
Contemporary orthodontics, William Proffit, 4th edition page 198