Abstract
Lipsitz, Dear and Zhao (1994) proposed a “one-step” Jackknife estimator of the variance based on Wu's (1986) jackknife and showed its asymptotic equivalence to the robust variance estimator of White (1982) and Liang and Zeger (1986). In this paper an asymptotically equivalent estimator is proposed which avoids the Newton-Raphson or Fisher scoring step of the estimator proposed by Lipsitz, Dear and Zhao. Hence, summation in univariate models can be avoided.
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References
Arminger, G. (1992). Residuals and Influential Points in Mean Structures Estimated With Pseudo maximum Likelihood Methods, in Fahrmeir et al.:Advances in GLIM and Statistical Modelling, New York: Springer, 20–26.
Arminger, G. (1995). Specification and Estimation of Mean Structures, in Arminger et al.:Handbook of Statistical Modeling for the Behavioral Sciences, New York: Plenum, 77–183.
Basilevsky, A. (1983). Applied Matrix Algebra in the Statistical Sciences, North-Holland: New York.
Cook, R. andWeisberg, S. (1982).Residuals and Influence in Regression. New York: Chapman and Hall.
Hoffmann, C. (1982). Die Berechnung von Tarifen für die Waldinventur.Forst. Centr.,101, 24–36.
Kublin, E. (1989). Verallgemeinerte lineare Regressionsmodelle mit inhomogener Fehlervarianz, in Pelz:Forest Statistics. Proceedings of the Conference on Forest Statistics, Mitteilungen der Abteilung für Forstliche Biometrie, Universität Freiburg, 174–186.
Laasasenaho, J. (1982).Taper Curve and Volume Functions for Pine, Spruce and Birch, Comm. Inst. Forest. Fenn.,108, Helsinki.
Liang, K.Y. andZeger, S. (1986). Longitudinal Data Analysis Using Generalized Linear Models.Biometrika,73, 13–22.
Lipsitz, S., Dear, K. andZhao, L. (1994). Jackknife Estimators of Variance for Parameter Estimates from Estimating Equations with Applications to Clustered Survival Data.Biometrics,50, 842–846.
McCullagh, P. and Nelder, J.A. (1989). Generalized Linear Models, 2nd edn. London: Chapman & Hall.
Moulton, L.H. andZeger, S.L. (1989). Analyzing Repeated Measures on Generalised Linear Models via the Bootstrap.Biometrics,45, 381–394.
Pregibon, D. (1981). Logistic Regression Diagnostics.The Annals of Statistics,9, 705–724.
Tukey, J.W. (1958). Bias and Confidence in Not-Quite Large Samples.Ann. Math. Stat.,29, 614.
White, H. (1982). Maximum likelihood estimation of misspecified models.Econometrica,50, 1–25.
Wu, C.F.U. (1986). Jackknife, Bootstrap and Other Resampling Methods in Regression Analysis.Ann. Stat.,14, 1261–1295.
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Ziegler, A. Practical considerations of the jackknife estimator of variance for generalized estimating equations. Statistical Papers 38, 363–369 (1997). https://doi.org/10.1007/BF02925276
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DOI: https://doi.org/10.1007/BF02925276