A Kalman filter model for single and two-stage repeated surveys (Q5893754)

The estimation of the population mean in two-stage repeated surveys is tackled by using a Bayesian framework. A general hypothesis in this problem is that the population does not change. If this is not accepted we have ''time-dependent'' parameters and characteristic vectors. Then the classical approach is not usable and some tools from stochastic processes should be used. This paper gives an alternative point of view when the characteristic vector depends on time, Y(t), and the parameter to be estimated is the population mean \(\theta\) (t). At fixed t some of the previous t-1 estimates should be available and the prediction of \(\theta\) (t) can be based on this information. A normal model fixes the randomness of the Y(t)'s and the estimator \({\hat \theta}\)(t)\(=\theta (t)-e_ i\) depends on the true parametric value and a random error with zero expectation. This relation characterizes the observation equation and the system equation relates \(\theta\) (t) with the previous t-1 means. A Kalman filter model is proposed and the posterior variance of \({\hat \theta}\)(t) is deduced. The problem is studied, when the variances are known or not, under single-stage sampling. The two-stage design with non- overlapping clusters is also studied. Under some additional hypotheses well known results from survey sampling are obtained as particular cases.