Figure 1 - uploaded by Raymond L. Czaplewski
Content may be subject to copyright.
Examples of distributions between a study variable and an auxiliary residual. The left-hand figure is a scatterplot between study variable y and auxiliary variable x. The right-hand figure portrays the same distribution after normalization.
Source publication
The Generalized Multivariate Difference estimator (GMDe) is a broad generalization of the univariate "difference estimator" described by Hansen et al. (1953:250-253) and Särndal et al. (1992:239-242). Difference estimators use population estimates of auxiliary variables to improve population estimates of correlated study variables.
Examples of au...
Similar publications
The Generalized Multivariate Difference estimator (GMDe) is designed for complex longitudinal sample surveys with auxiliary variables. An example is a National Forest Inventory (NFI) that includes annual re‑measurements for panels of sample field plots, plus remotely sensed data for disturbance detection, plus time‑series of predictions from a dete...
Citations
... In addition, population estimates from a probability sample and a design-consistent estimator, such as the Horvitz-Thompson estimator, are identified as "π-estimates" from a "π-estimator" respectively. Some derivations and other details are available in Czaplewski (2020aCzaplewski ( , 2020bCzaplewski ( , 2021 ...
The Generalized Multivariate Difference estimator (GMDe) is designed for complex longitudinal sample surveys with auxiliary variables. An example is a National Forest Inventory (NFI) that includes annual re‑measurements for panels of sample field plots, plus remotely sensed data for disturbance detection, plus time‑series of predictions from a deterministic ecosystem model for undisturbed plots. GMDe is a multivariate extension of an estimator published by Hansen, Hurwitz and Madow in 1953. GMDe is a robust alternative to model‑assisted and model‑based estimators. GMDe is closely related to the multivariate composite estimator and the Kalman filter update. GMDe is a simple linear transformation of a large vector that contains population estimates for study variables and auxiliary variables in either a finite or infinite population. The initial coefficient matrix in the transformation specifically minimizes the variance for each population estimate. GMDe modifies that matrix to impose inequality constraints and mitigate influence of outliers.
