Gil, María Angeles A note on stratification and gain in precision in estimating diversity from large samples. (English) Zbl 0696.62261 Commun. Stat., Theory Methods 18, No. 4, 1521-1526 (1989). Several indices of entropy have been suggested in the literature as weighted diversity measures of a population with respect to a classification process. When the population is finite but too large to be censused, the diversity with respect to a given classification process must be estimated from a sample. In this note, on the basis of an asymptotic study of the sample indices in the stratified random sampling, we are going to confirm that when we deal with large samples one can guarantee a gain in precision from stratified random over simple random sampling. This gain becomes considerable when the “inaccuracy” between the frequency vector in each stratum and that in the whole population, varies greatly from stratum to stratum. Cited in 13 Documents MSC: 62H30 Classification and discrimination; cluster analysis (statistical aspects) 62D05 Sampling theory, sample surveys Keywords:asymptotic normality; propotional allocation; entropy measures; estimation; diversity; stratified random sampling × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Bhargava T. N., Appl. Math. Comput 3 pp 1– (1977) · Zbl 0403.62018 · doi:10.1016/0096-3003(77)90008-X [2] Bishop Y. M. M., Discrete Multivariate Analysis: Theory and Practice (1975) [3] Bourguignon F., Eccnometrica 47 pp 901– (1979) · Zbl 0424.90013 · doi:10.2307/1914138 [4] Gil M. A., RAJ.R.O.-Rech, Opèer 20 (3) pp 257– (1986) [5] Good I. J., Biometrika 40 (3) pp 237– (1953) · Zbl 0051.37103 · doi:10.1093/biomet/40.3-4.237 [6] Havrda J., Kybernetika 3 (3) pp 30– (1967) [7] Kerridge D. F., J. Royal Stat. Soc, Ser. B 23 (3) pp 184– (1961) [8] Nayak T. K., Commun. Statist. -Theory and Methods 14 (1) pp 203– (1985) · Zbl 0561.62004 · doi:10.1080/03610928508828905 [9] Patil G. P., J. Am. Stat. Assoc 77 (379) pp 548– (1982) · doi:10.1080/01621459.1982.10477845 [10] Pielou E.C., Ecological Diversity (1975) [11] Rao C. R., Sankhya, Ser. A 44 (1) pp 1– (1982) [12] Ramie P. N., J. Ann. Inst. Statist. Math 25 (1) pp 205– (1973) · Zbl 0338.94016 · doi:10.1007/BF02479370 [13] Routledge R. D., J. Theor. Biol 76 (1) pp 503– (1979) · doi:10.1016/0022-5193(79)90015-8 [14] Shannon C. E., Bell System Tech. J 27 (1) pp 379– (1948) · Zbl 1154.94303 · doi:10.1002/j.1538-7305.1948.tb01338.x [15] Simpson E. H., Nature 163 (1) pp 688– (1949) · Zbl 0032.03902 · doi:10.1038/163688a0 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.