Abstract
We examine the performance of the standard tests—the mean test, the t-test, the Wilcoxon test and the sign test—for testing that the measure of central tendency of a distribution is zero. We do this by comparing the Bahadur slopes in a contaminated normal model. We first establish the large deviation principle (LDP) and then calculate the Bahadur slopes for the standard test statistics when the observations come from a contaminated normal distribution. An examination of tables of Bahadur efficiencies reveals that the Wilcoxon test outperforms other tests in a neighborhood of the null hypothesis, even in the presence of moderate contamination, but not uniformly over the whole alternative hypothesis.
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© 1997 Birkhäuser Boston
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Chaganty, N.R., Sethuraman, J. (1997). The Large Deviation Principle for Common Statistical Tests Against a Contaminated Normal. In: Panchapakesan, S., Balakrishnan, N. (eds) Advances in Statistical Decision Theory and Applications. Statistics for Industry and Technology. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2308-5_16
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DOI: https://doi.org/10.1007/978-1-4612-2308-5_16
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-7495-7
Online ISBN: 978-1-4612-2308-5
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