Abstract
A common problem faced by an experimenter is one of comparing several populations (processes, treatments). Suppose that there are k(≥ 2) populations π1,… ,πk and for each i, πi. is characterized by the value of a parameter of interest, say θi.. The classical approach to this problem is to test the homogeneity hypothesis H0:θ1 =… = θk. However, the classical tests of homogeneity are inadequate in the sense that they do not answer a frequently encountered experimenter’s question, namely, how to identify the “best” population or how to select the more promising (worthwhile) subset of the populations for further experimentation. These problems are known as ranking and selection problems. The formulation of ranking and selection procedures has been accomplished generally using either the indifference zone approach (see Bechhofer (1954)) or the subset selection approach (see Gupta (1956, 1965)). A discussion of their differences and various modifications that have taken place since then can be found in Gupta and Panchapakesan (1979).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bechhofer, R. E., 1954, A single-sample multiple decision procedure for ranking means of normal populations with known variances, Ann. Math, Statist., 25:16–39.
Berger, J., and Deely, J. J., 1986, A Bayesian approach to ranking and selection of related means with alternatives to AOV methodology, Technical Report #86-8, Department of Statistics, Purdue University, West Lafayette, Indiana.
Bickelj P. J. and YahaVj J. A., 1977, On selecting a subset of good populations, Statistical Decision Theory and Related Topics-II (Eds. S.S. Gupta and D. S. Moore), Academic, New York, 37–55.
Chernoff, H., and Yahav, J. A., 1977, A subset selection problem employing a new criterion. Statistical Decision Theory and Related Topics-II (Eds. S. S. Gupta and D. S. Moore), Academic, New York, 93–119.
Deely, J. J., 1965, Multiple decision procedures from an empirical Bayes approach, Ph.D. Thesis (Mimeo. Ser. No. 45), Department of Statistics, Purdue University, West Lafayette, Indiana.
Deely, J. J., and Gupta, S. S., 1968, On the properties of subset selection procedures, Sankhyā, A30:37–50.
Goel, P. K., and Rubin, H. 1977, On selecting a subset containing the best population--A Bayesian approach, Ann. Statist., 5:969–983.
Grenander, U., 1956, On the theory of mortality measurement, Part II. Skand. Akt., 39:125–153.
Gupta, S. S., 1956, On a decision rule for a problem in ranking means, Ph.D. Thesis (Mimeo. Ser. No. 150), Inst. of Statist., University of North Carolina, Chapel Hill.
Gupta, S. S., 1965, On some multiple decision (selection and ranking) rules,Technometries, 7:225–245. «
Gupta, S. S., and Hsiao, P., 1981, On T-minimax, minimax, and Bayes procedures for selecting populations close to a control, Sankhyā, B43:291–318.
Gupta, S. S., and Hsiao, P., 1983, Empirical Bayes rules for selecting good populations, J. Statist. Plan. Infer., 8:87–101.
Gupta, S. S., and Hsu, J. C, 1978, On the performance of some subset selection procedures, Commun. Statist.-Simula. Computa., B7(6):561–591.
Gupta, S. S., and Liang, T., 1984, Empirical Bayes rules for selecting good binomial populations, to appear in The Proceedings of the Symposium on Adaptive Statistical Procedures and Related Topics.
Gupta, S. S., and Liang, T., 1986, Empirical Bayes rules for selecting the best binomial population, to appear in Statistical Decision Theory and Related Topics-IV (Eds. S. S. Gupta and J. O. Berger).
Gupta, S. S., and Mieseke, K., 1984, On two-stage Bayes selection procedures, Sankhyā, B46:123–134.
Gupta, S. S., and Panchapakesan, S., 1979, “Multiple Decision Procedures”, Wiley, New York.
Gupta, S. S., and Yang, H. M., 1985, Bayes-P* subset selection procedures for the best population, J. Statist. Plan. Infer., 12:213–233.
Miescke, K., 1979, Bayesian subset selection for additive and linear loss functions, Commun. Statist.-Theor. Meth., A8(12):1205–1226.
Robbins, H., 1956, An empirical Bayes approach to statistics, Proc. Third Berkeley Symp. Math. Probab., University of California Press, 155–163.
Robbins, H., 1964, The empirical Bayes approach to statistical decision problems, Ann. Math. Statist., 35:1–19.
Robbins, H., 1983, Some thoughts on empirical Bayes estimation, Ann. Statist., 11:713–723.
Samuel, E., 1963, An empirical Bayes approach to the testing of certain parametric hypothesis, Ann. Math. Statist., 34:1370–1385.
Van Ryzin, J., and Susarla, V., 1977, On the empirical Bayes approach to multiple decision problems, Ann. Statist., 5:172–181.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1987 Plenum Press, New York
About this chapter
Cite this chapter
Gupta, S.S., Liang, T. (1987). On Some Bayes and Empirical Bayes Selection Procedures. In: Viertl, R. (eds) Probability and Bayesian Statistics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-1885-9_24
Download citation
DOI: https://doi.org/10.1007/978-1-4613-1885-9_24
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4612-9050-6
Online ISBN: 978-1-4613-1885-9
eBook Packages: Springer Book Archive