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December, 1987 Heteroscedasticity-Robustness of Jackknife Variance Estimators in Linear Models
Jun Shao, C. F. J. Wu
Ann. Statist. 15(4): 1563-1579 (December, 1987). DOI: 10.1214/aos/1176350610


The asymptotic unbiasedness and consistency of three types of jackknife variance estimators in the presence of error variance heteroscedasticity in linear models are studied. The results are given in terms of the number of observations deleted and measures of imbalance of the model. The consistency of a class of Wu's weighted jackknife variance estimators for nonlinear parameters is also studied. A necessary and sufficient condition is given for the asymptotic unbiasedness and consistency of the unweighted delete-1 jackknife variance estimator and Hinkley's weighted delete-1 jackknife variance estimator. This condition is more stringent than those required for Wu's weighted jackknife. Comparison of the three delete-1 jackknife variance estimators in terms of their biases also favors the latter method.


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Jun Shao. C. F. J. Wu. "Heteroscedasticity-Robustness of Jackknife Variance Estimators in Linear Models." Ann. Statist. 15 (4) 1563 - 1579, December, 1987.


Published: December, 1987
First available in Project Euclid: 12 April 2007

zbMATH: 0651.62064
MathSciNet: MR913574
Digital Object Identifier: 10.1214/aos/1176350610

Primary: 62J05
Secondary: 62F35

Rights: Copyright © 1987 Institute of Mathematical Statistics


Vol.15 • No. 4 • December, 1987
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