Consider the random group estimator of the variance from Section 9.2.2. The parameter of interest is =U. A simple random sample with replacement of

Consider the random group estimator of the variance from Section 9.2.2. The parameter of interest is θ =U. A simple random sample with replacement of size n is taken from the population. The sample is divided into R random groups, each of size m. Let ˆθ r be the sample mean of them observations in random group r, let

And let Ṽ2 (ˆθ) be the variance estimator defined in (9.5). Show that

Where