Multivariate dual to ratio type estimators using arithmetic, geometric   and harmonic means in simple random sampling
  Auxiliary variable is extensively used in survey sampling to improve the precision of estimates. Whenever there is availability of auxiliary information, we want to utilize it in the method of estimation to obtain the most efficient estimator. In this paper using multi-auxiliary information we have proposed estimators based on arithmetic, geometric and harmonic mean. It was also shown that estimator based on harmonic and geometric means are more biased than estimator based on arithmetic mean under certain conditions. However, the MSE of all three estimators are same up to the first order of approximation. 
Rajesh Singh, Prayas Sharma
stat.AP