A balanced multi-level rotation sampling design and its efficient composite estimators

We present a multi-level rotation sampling design which includes most of the existing rotation designs as special cases. When an estimator is defined under this sampling design, its variance and bias remain the same over survey months, but it is not so under other existing rotation designs. Using the properties of this multi-level rotation design, we derive the mean squared error (MSE) of the generalized composite estimator (GCE), incorporating the two types of correlations arising from rotating sample units. We show that the MSEs of other existing composite estimators currently used can be expressed as special cases of the GCE. Furthermore, since the coefficients of the GCE are unknown and difficult to determine, we present the minimum risk window estimator (MRWE) as an alternative estimator. This MRWE has the smallest MSE under this rotation design and yet, it is easy to calculate. The MRWE is unbiased for monthly and yearly changes and preserves the internal consistency in total. Our numerical study shows that the MRWE is as efficient as GCE and more efficient than the existing composite estimators and does not suffer from the drift problem [Fuller W.A., Rao J.N.K., 2001. A regression composite estimator with application to the Canadian Labour Force Survey. Surv. Methodol. 27 (2001) 45-51] unlike the regression composite estimators.