Generalized Multivariate Difference Estimator (GMDe): The Recursive Algorithm (rGMDe)

By Raymond L Czaplewski

This book introduces the recursive Generalized Multivariate Difference estimator (GMDe) , which is a new statistical method for complex sample surveys with high dimensions. rGMDe is simple, robust, adaptable, and well suited for long-term production of official statistics. GMDe reduces uncertainty in numerous population estimates for the analyst's study variables that are well correlated numerous auxiliary variables from less costly sources, such as remote sensors, deterministic models, administrative records, found data, "big data", and supplemental sampling frames. GMDe is a type of multivariate composite estimator. It weights population estimates rather than individual sampling units. GMDe is a pioneering alternative to mixed estimators, calibration estimators, and regression estimators. GMDe uses a vector of population estimates for auxiliary residuals and a matrix of "optimal" weights, i.e ., "the model", to adjust a vector of population estimates for the study variables. The latter may include partitions for different time periods, networks of hierarchical analysis domains, and small sub-populations. The survey statistician can design different sample survey and census systems for different analysis objectives and measurement technologies, and each can evolve over time. rGMDe integrates the time-series of multivariate population estimates from multiple systems. The analyst can use rGMDe to gain new insights. Exploratory analyses of orthogonal auxiliary residuals can reveal differences between expected and estimated population parameters. The relative strengths of rGMDe composite weights allow the analyst to compare competing sets of hypotheses, such as deterministic prediction models with different assumptions regarding population dynamics. The covariance matrix among auxiliary residuals can be rank-deficient with strong collinearities. Rather than the matrix inverse, rGMDe uses a recursive sequence of scalar inversions, one recursion for each auxiliary residual. Within each recursion, rGMDe uses efficient stepwise selection among the remaining auxiliary residuals, without analyst intervention. rGMDe censors spurious or weak correlations between study variables and the auxiliary residual. rGMDe relaxes the minimum variance criterion to impose minmax inequality constraints, mitigate outliers, and assure a coherent population covariance matrix. Therefore, rGMDe reliably accommodates large vectors of population estimates.

• Format: Hardcover
• Language: English
• ISBN: B0CVGDMS77
• ISBN13: 9798874319038
• Release Date: February 2024
• Publisher: Independently published
• Length: 244 Pages
• Weight: 1.53 lbs.
• Dimensions: 11.0" x 0.7" x 8.3"