Summary
The bootstrap estimation for variance and its robustness in linear regression is considered. It is shown that the bootstrap approximation to the distribution of the estimator of the error variance, based on the least squared estimator, is robust over the Mallows neighborhood.
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References
Babu, G. (1984), Bootstrapping statistics with linear combinations of chi-squares as weak limit.Sankhya, ser. A 46, 85–93.
Babu, G. andSingh, K. (1983), Inference on means using the bootstrap.Ann. Statist. 11, 999–1003.
Bickel, P. andFreedman, D. (1981), Some asymptotic theory for the bootstrap.Ann. Statist. 9, 1196–1217.
Bickel, P., Gotze, F. andvan Zwet, W. (1986), The Edgeworth expansion for U-statistics of degree two.Ann. Statist. 14, 1463–1484.
Efron, B. (1979), Bootstrap methods: another look at the Jackknife.Ann. Statist 7, 1–26.
Hampel, F. (1971), A general qualitative definition of robustness.Ann. Math. Statist. 42, 1887–1896.
Helmers, R. (1991), On the Edgeworth expansion and the bootstrap approximation for a studentized U-statistic.Ann. Statist. 19 470–484.
Heyde, H. (1980),Martingale limit theory and its application. Academic Press, New York.
Huber, P. (1981),Robust Statistics. Wiley, New York.
Loeve, M. (1977),Probability theory I, Springer-Verlag, New York.
Mallows, C. (1972), A note on asymptotic joint normality.Ann. Math. Statist. 43, 508–515.
Zhao, L. (1982), Necessary and sufficient conditions for the strong consistency of the estimate of error variance in linear models.Scientia Sinica 25, 449–454.
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Partially supported by Univeristy of Kansas general research fund.
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He, K. The robustness of bootstrap estimator of variance. J. It. Statist. Soc. 4, 183–193 (1995). https://doi.org/10.1007/BF02589101
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DOI: https://doi.org/10.1007/BF02589101