A non-negativity criterion for a certain variance-estimator

Summary A well-known strategy for the estimation of a finitepopulation-total is to use the ratioestimator based on the Midzuno-Sen scheme of sampling. Unbiased estimators of the variance of this estimator are not always non-negative though they are required to be so from practical considerations. One such estimator is shown to be non-negative for all variate-values under an easily verifiable condition on the parameters of the sampling strategy.