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To estimate the population mean when sampling a heterogeneous population and in the absence of a priori information on auxiliary variables, exponential-ratio multivariate estimators are associated under double stratified sampling with two auxiliary variables. Their biases and mean square errors are expressed and simulated. These mean square errors are smaller (the efficiencies are higher) than those of the sample mean estimator and those of other ratio estimators when the correlation between the study and the auxiliary variables exceeds 0.1 in absolute value. In particular, the proposed estimators are more efficient for low correlations between the study and the auxiliary variables. The gain in efficiency reaches a factor of 230.4% on an empirical dataset where the study variable is weakly correlated with each of the two auxiliary variables, and 182.1% on another empirical dataset where it is strongly correlated.

Multivariate ratio exponential estimators of the population mean under stratified double sampling