Variance Estimation in Partially Systematic Sampling

Systematic sampling is very convenient in many practical situations, but does not provide a satisfactory estimator of the variance of the sample mean except when additional assumptions are made. A method is proposed to estimate the mean of a finite population and to estimate the variance of this estimate, using a systematic sample and a simple random sample drawn from the remaining population. It is shown that both estimators are unbiased. This method provides also an unbiased, positive estimator of the population variance. A comparison with multiple-start systematic sampling is made. Some numerical results for artificial populations are given.