Quantile estimation in two-phase sampling

The estimation of quantiles in two-phase sampling with arbitrary sampling design in each of the two phases is investigated. Several ratio and exponentiation type estimators that provide the optimum estimate of a quantile based on an optimum exponent αα are proposed. Properties of these estimators are studied under large sample size approximation and the use of double sampling for stratification to estimate quantiles can also be seen. The real performance of these estimators will be evaluated for the three quartiles on the basis of data from two real populations using different sampling designs. The simulation study shows that proposed estimators can be very satisfactory in terms of relative bias and efficiency.