Acknowledgements. This research was supported by the Galician Official Statistical Institute (IGE) and by a Spanish grant from the Ministerio de Ciencia y Tecnología (MTM2011-22392). The authors would like to thank two anonymous referees for suggestions that helped to improve the quality of this paper.
Generalised Variance Function Estimation for Binary Variables in Large-Scale Sample Surveys
Article first published online: 20 DEC 2012
© 2012 Australian Statistical Publishing Association Inc. Published by Wiley Publishing Asia Pty Ltd.
Australian & New Zealand Journal of Statistics
Volume 54, Issue 3, pages 301–324, September 2012
How to Cite
Cao, R., Vilar, J. A. and Vilar, J. M. (2012), Generalised Variance Function Estimation for Binary Variables in Large-Scale Sample Surveys. Australian & New Zealand Journal of Statistics, 54: 301–324. doi: 10.1111/j.1467-842X.2012.00682.x
- Issue published online: 20 DEC 2012
- Article first published online: 20 DEC 2012
- least logarithmic squares;
- local reciprocal fit;
- nonparametric regression;
- parametric regression
Generalised variance function (GVF) models are data analysis techniques often used in large-scale sample surveys to approximate the design variance of point estimators for population means and proportions. Some potential advantages of the GVF approach include operational simplicity, more stable sampling errors estimates and providing a convenient method of summarising results when a high number of survey variables is considered. In this paper, several parametric and nonparametric methods for GVF estimation with binary variables are proposed and compared. The behavior of these estimators is analysed under heteroscedasticity and in the presence of outliers and influential observations. An empirical study based on the annual survey of living conditions in Galicia (a region in the northwest of Spain) illustrates the behaviour of the proposed estimators.