Abstract
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.
Article PDF
Avoid common mistakes on your manuscript.
References
Cochran, W. G., Sampling Techniques (3rd ed.) (John Wiley & Sons, New York, NY, 1977).
Bhatti, M., Cluster Effects in Mining Complex Data. (Nova Science Publisher’s, New York, NY, 2012).
Scott, A. J., and Holt, D., The Effect of Two-Stage Sampling on Ordinary Least Squares Methods, Journal of the American Statistical Association, 77(380), (1982) 848–854.
Feller, W., An Introduction to Probability Theory and its Applications (Vol. 1, 3rd ed.) (John Wiley & Sons, New York, NY, 1967).
SAS Institute, Inc., SAS/STAT 9.2 User’s Guide, Chapter 92 (SAS Institute, Cary, NC, 2009).
Levene, H., Contributions to Probability and Statistics: Essays in Honor of Harold Hotelling, eds. Olkin, Hotelling, et al (Stanford, CA: Stanford University Press, Stanford, CA, 1960), pp. 278–292.
White, H., A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity, Econometrica, 48(4), (1980) 817–838.
Breusch, T. S., and Pagan, A. R., A Simple Test for Heteroscedasticity and Random Coefficient Variation, Econometrica, 47(5), (1979) 1287–1294.
IBM Corporation, IBM SPSS Algorithms, t Test Algorithms, One Sample t Test, [online]. Available at: http://129.8.241.71:56773/help/index.jsp?topic=%2Fcom.ibm.spss.statistics.algorithms%2Falg_introduction.htm
Author information
Authors and Affiliations
Rights and permissions
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
About this article
Cite this article
Stengel, D.N., Chaffe-Stengel, P. Estimating Per Capita Rates Using Aggregate Measurements From Groups of Diverse Compositions. J Stat Theory Appl 14, 192–203 (2015). https://doi.org/10.2991/jsta.2015.14.2.7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.2991/jsta.2015.14.2.7