Abstract
Based on shrinkage and preliminary test rules, various estimators are proposed for estimation of several intraclass correlation coefficients when independent samples are drawn from multivariate normal populations. It is demonstrated that the James-Stein type estimators are asymptotically superior to the usual estimators. Furthermore, it is also indicated through asymptotic results that none of the preliminary test and shrinkage estimators dominate each other, though they perform relatively well as compared to the classical estimator. The relative dominance picture of the estimators is presented. A Monte Carlo study is performed to appraise the properties of the proposed estimators for small samples.
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References
Ahmed, S. E. (1991). To pool or not to pool: The discrete data, Probability and Statistics Letters, 11, 233-237.
Ahmed, S. E. (1992a). Shrinkage preliminary test estimation in multivariate normal distributions, J. Statist. Comput. Simulation., 43, 177-195.
Ahmed, S. E. (1992b). Large-sample pooling procedure for correlation, The Statistician, 41, 425-438.
Bancroft, T. A. (1944). On biases in estimation due to use of preliminary test of significance, Ann. Math. Statist., 15, 190-204.
Bancroft, T. A. and Han, C. P. (1977). Inference based on conditional specification: A note and a bibliography, International Statistical Review, 45, 117-127.
Barnes, R. and Gillingham, R. (1984). Demographic effects in demand analysis: estimation of the quadratic expenditure system, Review of Economics and Statistics, 66, 591-601.
Donner, A. (1986). A review of inference procedure for the intra class correlation coefficient in the one-way random effect model, International Statistical Review, 54, 67-82.
Donner, A. and Koval, J. J. (1980). The estimation of intraclass correlation in the analysis of family data, Biometrics, 36, 19-25.
Elston, R. C. (1975). Correlation between correlations, Biometrika, 62, 133-148.
Fisher, R. A. (1958). Statistical methods for research workers, Oliver & Boyd, Edinburgh.
Gupta, A. K., Saleh, A. K. M. E. and Sen, P. K. (1989). Improved estimation in a contingency table: Independence structure. J. Amer. Statist. Assoc., 84, 525-532.
Han, C. P., Rao, C. V. and Ravichandran J. (1988). Inference based on conditional specification: A second bibliography, Comm. Statist. Theory Methods, 17, 1945-1964.
James W. and Stein, C. (1961). Estimation with quadratic loss. Proc. the Fourth Berkeley Sym. on Math. Statist. Prob., 1, University of California Press, Berkeley, 361-379.
Judge, G. G. and Bock, M. E. (1978). The Statistical Implication of Pre-test and Stein-rule Estimators in Econometrics, North Holland, Amsterdam.
Katapa, R. S. (1993). A test of hypothesis on familial correlations, Biometrics, 49, 569-576.
Konishi, S. (1985). Normalizing and variance stabilizing transformations for intraclass correlations, Ann. Inst. Statist. Math., 37, 87-94.
Konishi, S. and Gupta, A. K. (1989). Testing the equality of several intraclass correlation coefficients, J. Statist. Plann. Inference, 21, 93-105.
Nicol, C. J. (1989). Testing a theory of exact aggregation, J. Bus. Econom. Statist., 7, 259-265.
Stigler, S. M. (1990). The 1988 Neyman memorial lecture: A Galtonian perspective on shrinkage estimators, Statist. Sci., 5, 147-155.
Survey of Family Expenditures Microdata Files, (1978, 1982, 1986, 1990 and 1992). Family expenditure surveys section, Statistics Canada, Ottawa, Canada.
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Ahmed, S.E., Gupta, A.K., Khan, S.M. et al. Simultaneous Estimation of Several Intraclass Correlation Coefficients. Annals of the Institute of Statistical Mathematics 53, 354–369 (2001). https://doi.org/10.1023/A:1012474807133
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DOI: https://doi.org/10.1023/A:1012474807133