Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-28T08:12:39.806Z Has data issue: false hasContentIssue false
  • English
  • Français

Restricted quasi-score estimating functions for sample survey data

Part of: Linear inference, regression Parametric inference

Published online by Cambridge University Press:  14 July 2016

Y.-X. Lin ,
D. Steel  and
R. L Chambers
Y.-X. Lin
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, NWS 2522, Australia. Email address: [email protected]
D. Steel
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, NWS 2522, Australia. Email address: [email protected]
R. L Chambers
Affiliation:
Southampton Statistical Sciences Research Institute, Building 39, University of Southampton, Highfield, Southampton SO17 1BJ, UK. Email address: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper applies the theory of the quasi-likelihood method to model-based inference for sample surveys. Currently, much of the theory related to sample surveys is based on the theory of maximum likelihood. The maximum likelihood approach is available only when the full probability structure of the survey data is known. However, this knowledge is rarely available in practice. Based on central limit theory, statisticians are often willing to accept the assumption that data have, say, a normal probability structure. However, such an assumption may not be reasonable in many situations in which sample surveys are used. We establish a framework for sample surveys which is less dependent on the exact underlying probability structure using the quasi-likelihood method.

Keywords

Estimating functionquasi-likelihoodsample survey

MSC classification

Primary: 62J12: Generalized linear models
Secondary: 62F99: None of the above, but in this section
Type
Part 2. Estimation methods
Information
Journal of Applied Probability , Volume 41 , Issue A: Stochastic Methods and their Applications , 2004 , pp. 119 - 130
Copyright
Copyright © Applied Probability Trust 2004 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Binder, D. A. and Patak, Z. (1994). Use of estimating functions for estimation from complex surveys. J. Amer. Statist. Assoc. 89, 1035–1043.Google Scholar
Breckling, J. U. et al. (1994). Maximum likelihood inference from sample survey data. Internat. Statist. Rev. 62, 349–363.Google Scholar
Godambe, V. P. and Heyde, C. C. (1987). Quasi-likelihood and optimal estimation. Internat. Statist. Rev. 55, 231–244.Google Scholar
Godambe, V. P. and Thompson, M. E. (1985). Logic of least squares revisited. Preprint.Google Scholar
Godambe, V. P. and Thompson, M. E. (1986). Parameters of superpopulation and survey population: their relationships and estimation. Internat. Statist. Rev. 54, 127–138.Google Scholar
Heyde, C. C. (1997). Quasi-likelihood and Its Application: A General Approach to Optimal Parameter Estimation. Springer, New York.Google Scholar
Heyde, C.C. and Lin, Y.-X. (1991). Approximate confidence zones in an estimating function context. In Estimating Functions (Oxford Statist. Sci. Ser. 7), ed. Godambe, V. P., Oxford University Press, pp. 161–168.Google Scholar
Lin, Y.-X. (1992). The method of quasi-likelihood. Doctoral Thesis, Australian National University, Canberra.Google Scholar
Lin, Y.-X. and Heyde, C. C. (1993). Optimal estimating functions and Wedderburn's quasi-likelihood. Commun. Statist. Theory Meth. 22, 2341–2350.Google Scholar
Lin, Y.-X. and Heyde, C. C. (1997). On space of estimating functions. J. Statist. Planning Infer. 63, 255–264.Google Scholar
Little, R. (2003). Bayesian methods for sample surveys subject to unit and item nonresponse. In Analysis of Survey Data , eds Chambers, R. L. and Skinner, C. J., John Wiley, Chichester, pp. 289–306.Google Scholar
Skinner, C. J., Holt, D. and Smith, T. M. F. (1989). Analysis of Complex Surveys. John Wiley, Chichester.Google Scholar