Numerically stable algorithm for combining census and sample estimates with the multivariate composite estimator

Abstract

The minimum variance multivariate composite estimator is a relatively simple sequential estimator for complex sampling designs (Czaplewski 2009). Such designs combine a probability sample of expensive field data with multiple censuses and/or samples of relatively inexpensive multi-sensor, multi-resolution remotely sensed data. Unfortunately, the multivariate composite estimator is vulnerable to numerical errors, which can cause infeasible or unreliable estimates (Grewal and Andrews 2001:Chapter 6). Numerical errors can exceed random estimation errors, which is especially dangerous if undetected (Bierman 1977:97). These problems are well known in the Kalman filter literature (e.g., Maybeck 1979), which is a generalization of the multivariate composite estimator. U-D factorization is a numerically robust solution (Bierman 1977).

Citation

Czaplewski, R. L. 2009. Numerically stable algorithm for combining census and sample estimates with the multivariate composite estimator. In: Finley, (ed.), Proceedings of the Symposium, Extending Forest Inventory and Monitoring Over Space and Time; May 19-22, 2009; Quebec City, Canada. Vienna, Austria: International Union of Forest Research Organizations (IUFRO), Division 4. 5 p. http://blue.for.msu.edu/meeting/proceed.php (August 17, 2009)