Least squares estimation for repeated surveys
Least squares estimation for repeated surveys is addressed. Several estimators of current level, change in level and average level over time are developed. Estimators include the recursive regression estimator, which is the best linear unbiased estimator based on all periods of the survey. The recursive regression estimator is designed to minimize the computational complexity associated with best linear unbiased estimation;We assume that the basic data consist of elementary estimators of the parameters of interest associated with different rotation groups and that their covariance structure is based on a components of variance model. Several theoretical results associated with the least squares estimation procedures are derived. In particular, we prove that (1) the recursive regression estimator of current level is optimal in the sense of minimum variance, and (2) the covariance matrix of the recursive least squares estimators converges to a positive definite matrix as the number of periods increases. The theoretical results are applicable to a wide range of estimation procedures and rotation designs;Several applications of the results to the estimation of selected labor force characteristics for the Current Population Survey are discussed. An estimated covariance structure for the data is used to compare alternative estimators and rotation designs. We address the issue of revision of previous estimates when additional observations become available at subsequent periods. We illustrate the fact that the revision of previous estimates provides optimal estimates of level and change which are internally consistent. We also describe a simple procedure for computing unrevised estimates of change whose variances are very close to those of the optimal estimator of change;The consequences of the time-in-sample effects on alternative estimators under assumptions of constant and time-varying time-in-sample effects are examined. Generally, the effect of including time-in-sample effects in the model is to increase the variance of the estimators. The increase in variance is a function of the type of restriction imposed and the length of period used to estimate the time-in-sample effects.