Abstract
In a one-way random-effects model, we frequently estimate the variance components by the analysis-of-variance method and then, assuming the estimated values are true values of the variance components, we estimate the population mean. The conventional variance estimator for the estimate of the mean has a bias. This bias can become severe in contaminated data. We can reduce the bias by using the delta method. However, it still suffers from a large bias. We develop a jackknife variance estimator which is robust with respect to data contamination.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Arvensen, J. N. and Layard, M. W. J. (1975). Asymptotically robust tests in unbalanced variance components models, Ann. Statist., 3, 1122–1134.
Arvensen, J. N. and Schmitz, T. (1970). Robust procedures for variance components problems using the jackknife, Biometrics, 26, 677–686.
Birkes, D., Seely, J. and Azzam, A. (1981). An efficient estimator of the mean in a two-stage nested model, Technometrics, 23, 143–148.
Efron, B. (1982). The Jackknife, the Bootstrap and Other Resampling Plans, SIAM, Philadelphia.
Hinkley, D. (1977). Jackknifing in unbalanced situations, Technometrics, 19, 285–292.
Kackar, R. N. and Harville, D. A. (1984). Approximations for standard errors of estimations of fixed and random effects in mixed linear models, J. Amer. Statist. Assoc., 79, 853–862.
Searle, S. R. (1971). Linear Models, Wiley, New York.
Simonoff, J. S. and Tsai, C. (1986). Jackknife-based estimators and confidence regions in nonlinear regression, Technometrics, 28, 103–122.
Swallow, W. H. (1981). Variances of locally minimum variance quadratic unbiased estimators (“MIVQUE's”) of variance components, Technometrics, 23, 271–283.
Swallow, W. H. and Monahan, J. F. (1984). Monte Carlo comparison of ANOVA, MIVQUE, REML, and ML estimators of variance components, Technometrics, 26, 47–57.
Wu, C. F. J. (1986). Jackknife, bootstrap and other resampling methods in regression analysis, Ann. Statist., 14, 1261–1295.
Author information
Authors and Affiliations
Additional information
This research was supported by the Korea Science and Engineering Foundation.
About this article
Cite this article
Lee, Y. Jackknife variance estimators of the location estimator in the one-way random-effects model. Ann Inst Stat Math 43, 707–714 (1991). https://doi.org/10.1007/BF00121649
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00121649