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Loss due to Missing Data in Efficiency of a Locally Optimal Test for Homogeneity with Respect to Very Rare Events
Prem S. Puri
Proceedings of the National Academy of Sciences of the United States of America
Vol. 67, No. 2 (Oct. 15, 1970), pp. 749-756
Published by: National Academy of Sciences
Stable URL: http://www.jstor.org/stable/59996
Page Count: 8
You can always find the topics here!Topics: Supernovae, Galaxies, Statistics, Random variables, Approximation, Statistical variance, Missing data, Probabilities, Mathematical problems, Mathematical constants
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With reference to observations of supernovae in galaxies, a locally optimal test for the hypothesis of homogeneity of the observational units with respect to occurrence of supernovae (treated as a very rare event) is obtained for the case where the data are available only for those galaxies where at least one supernova is observed. It is shown that the loss in the asymptotic efficiency of the test due to lack of reporting of galaxies with no supernovae is very heavy and in fact is infinite for the case of very rare events.
Proceedings of the National Academy of Sciences of the United States of America © 1970 National Academy of Sciences