Estimation of change with partially overlapping and spatially balanced samples

Spatially balanced samples are samples that are well-spread in some available auxiliary variables. Selecting such samples has been proven to be very efficient in estimation of the current state (total or mean) of target variables related to the auxiliary variables. As time goes, or when new auxiliary variables become available, such samples need to be updated to stay well-spread and produce good estimates of the current state. In such an update, we want to keep some overlap between successive samples to improve the estimation of change. With this approach, we end up with partially overlapping and spatially balanced samples. To estimate the variance of an estimator of change, we need to be able to estimate the covariance between successive estimators of the current state. We introduce an approximate estimator of such covariance based on local means. By simulation studies, we show that the proposed estimator can reduce the bias compared to a commonly used estimator. Also, the new estimator tends to become less biased when reducing the local neighborhood size.