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Alternative confidence intervals for the total of a skewed biological population
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Mathematical Statistics .
2004 (English)In: Ecology, ISSN 0012-9658, Vol. 85, no 11, 3166-3171 p.Article in journal (Refereed) Published
Abstract [en]

In a 1999 Ecology article, T. G. Gregoire and O. Schabenberger addressed the problem of obtaining truly symmetric confidence intervals for the total of a positively skewed biological population under simple random sampling. Their simulation study revealed that the skewness induced a substantial positive correlation between the estimator of the total and the estimator of its variance. This caused the standard nominally symmetric t-based intervals, based on approximate normality of the estimator of the total, to be highly unbalanced, i.e., intervals much more often missed from below than from above. To better cope with this situation I suggest an alternative confidence interval procedure that takes into account and adjusts for the induced correlation. A simulation study based on one of the populations used by Gregoire and Schabenberger shows that the resulting adjusted intervals have more balanced noncoverage probabilities and often higher coverage probability than the standard intervals in cases of substantial correlation. I also provide an example of an unequal probability design using auxiliary information, where there is much less need for an adjustment.

Place, publisher, year, edition, pages
2004. Vol. 85, no 11, 3166-3171 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-23071Local ID: 2460OAI: oai:DiVA.org:liu-23071DiVA: diva2:243384
Available from: 2009-10-07 Created: 2009-10-07 Last updated: 2011-01-12

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Andersson, Per Gösta

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