The DOI matches its Crossref record; 15 of the 15 references it cites were found in a registry or an index.
Small-Sample Adjustments for Wald-Type Tests Using Sandwich Estimators
Abstract
The sandwich estimator of variance may be used to create robust Wald-type tests from estimating equations that are sums of K independent or approximately independent terms. For example, for repeated measures data on K individuals, each term relates to a different individual. These tests applied to a parameter may have greater than nominal size if K is small, or more generally if the parameter to be tested is essentially estimated from a small number of terms in the estimating equation. We offer some practical modifications to these robust Wald-type tests, which asymptotically approach the usual robust Wald-type tests. We show that one of these modifications provides exact coverage for a simple case and examine by simulation the modifications applied to the generalized estimating equations of Liang and Zeger (1986), conditional logistic regression, and the Cox proportional hazard model.
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Citations
Cites
Longitudinal data analysis using generalized linear models
LIANG, K.-Y., & ZEGER, S. L. (1986) · Biometrika · doi:10.1093/biomet/73.1.13 · Cited by 18,550
The Robust Inference for the Cox Proportional Hazards Model
Lin, D. Y., & Wei, L. J. (1989) · Journal of the American Statistical Association · doi:10.1080/01621459.1989.10478874 · Cited by 2,695
Matrix Algebra Useful for Statistics
Schmee, J. (1985) · Technometrics · doi:10.1080/00401706.1985.10488022 · Cited by 775
Matrix Algebra Useful for Statistics.
Green, P. J., & Searle, S. R. (1983) · Biometrics · doi:10.2307/2531366 · Cited by 528
A Covariance Estimator for GEE with Improved Small‐Sample Properties
Mancl, L. A., & DeRouen, T. A. (2001) · Biometrics · doi:10.1111/j.0006-341x.2001.00126.x · Cited by 493
Review of Software to Fit Generalized Estimating Equation Regression Models
Horton, N. J., & Lipsitz, S. R. (1999) · The American Statistician · doi:10.1080/00031305.1999.10474451 · Cited by 387
Hrong-Tai Fai, A., & Cornelius, P. L. (1996) · Journal of Statistical Computation and Simulation · doi:10.1080/00949659608811740 · Cited by 260
Performance of Generalized Estimating Equations in Practical Situations
Lipsitz, S. R., Fitzmaurice, G. M., Orav, E. J., & Laird, N. M. (1994) · Biometrics · doi:10.2307/2533218 · Cited by 219
Likelihood calculations for matched case-control studies and survival studies with tied death times
GAIL, M. H., LUBIN, J. H., & RUBINSTEIN, L. V. (1981) · Biometrika · doi:10.1093/biomet/68.3.703 · Cited by 209
Fay, M. P., Freedman, L. S., Clifford, C. K., et al. (1997) · PubMed · Cited by 198
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Fortin, D., Beyer, H. L., Boyce, M. S., Smith, D. W., Duchesne, T., & Mao, J. S. (2005) · Ecology · doi:10.1890/04-0953 · Cited by 1,351
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Murray, D. M., Varnell, S. P., & Blitstein, J. L. (2004) · American Journal of Public Health · doi:10.2105/ajph.94.3.423 · Cited by 677
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Metadata
- Authors
- Fay, M. P., & Graubard, B. I.
- Venue
- Biometrics
- Publisher
- Oxford University Press (OUP)
- Published
- 2001-12
- Volume
- 57
- Issue
- 4
- Pages
- 1198-1206
- ISSN
- 0006-341X (ISSN-L)
- OpenAlex
- W2003583202
- Cited by
- 306
- References
- 15
- FWCI
- 4.09
- Type
- journal article
- Language
- en
- Open access
- closed
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