Estimation for time series subject to the error of rotation sampling
Édina Shisue Miazaki · 1985
The use of repeated surveys to estimate the population mean of a variable over time is approached as a time series problem. A survey carried out at time t yields an estimate Y(,t) of the population mean X(,t). We write Y(,t) = X(,t) + u(,t), where u(,t) is the survey error of estimation. If X(,t) follows a stochastic model, the problem of estimating X(,t) becomes one of estimating a time series observed subject to measurement error. In this work X(,t) is postulated to be an autoregressive process;In rotation sampling designs, the measurement error u(,t) can be modeled as a moving average process. An efficient estimation method, based upon the properties of the least squares estimators of an autoregressive moving average, is developed for the parameters of the X(,t) process. A Monte Carlo study examining the estimations method was conducted. The distributional properties of the estimators showed reasonable agreement with the asymptotic theory for samples of thirty or more observations from the first order autoregressive process;Application of time series estimation techniques to the National Crime Survey is considered. One set of estimates suggests that the use of time series procedures produces sizable gains in efficiencies for estimates of yearly victimization level constructed in the first three months of the following year.