Estimating Per Capita Rates Using Aggregate Measurements From Groups of Diverse Compositions

• Published in: Journal of statistical theory and applications Vol. 14; no. 2; pp. 192 - 203
• Main Authors: Stengel, Donald N., Chaffe-Stengel, Priscilla
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.06.2015; Springer Nature B.V; Springer
• Subjects: Correlation coefficients; Estimation; Grouped data; Research Article; Sampling; Estimation; Grouped data; 62D99; 62-07; 2010 Mathematics Subject Classification; 62F10; Sampling
• ISSN: 1538-7887; 2214-1766; 2214-1766; 1538-7887
• DOI: 10.2991/jsta.2015.14.2.7

This paper considers the problem of estimating a variable mean for a population of elements where data are only available as aggregate sums for groups of multiple elements. The proposed model addresses an additional complication created when the group measure includes the contribution of diverse elements that were only partially in operation or present as part of the group during the measurement period. The model also accounts for statistical dependency between the contributions of individuals belonging to the same group. The degree of statistical dependency is reflected in a correlation coefficient parameter, which, while not observable, can be adjusted to reduce heteroscedasticity in the group data. A simple example is provided to illustrate the model.