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Asymptotic Relative Efficiency in Testing

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International Encyclopedia of Statistical Science

Asymptotic Relative Efficiency of Two Tests

Making a substantiated choice of the most efficient statistical test of several ones being at the disposal of the statistician is regarded as one of the basic problems of Statistics. This problem became especially important in the middle of XX century when appeared computationally simple but “inefficient” rank tests.

Asymptotic relative efficiency (ARE) is a notion which enables to implement in large samples the quantitative comparison of two different tests used for testing of the same statistical hypothesis. The notion of the asymptotic efficiency of tests is more complicated than that of asymptotic efficiency of estimates. Various approaches to this notion were identified only in late forties and early fifties, hence, 20–25 years later than in the estimation theory. We proceed now to their description.

Let {T n } and {V n } be two sequences of statistics based on n observations and assigned for testing the null-hypothesis Hagainst the...

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Author information

Authors and Affiliations

  1. St. Petersburg University, St. Petersburg, Russia

    Yakov Nikitin (Professor, Chair of Probability and Statistics)

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  1. Yakov Nikitin
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Editors and Affiliations

  1. Department of Statistics and Informatics, Faculty of Economics, University of Kragujevac, City of Kragujevac, Serbia

    Miodrag Lovric

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© 2011 Springer-Verlag Berlin Heidelberg

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Nikitin, Y. (2011). Asymptotic Relative Efficiency in Testing. In: Lovric, M. (eds) International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04898-2_127

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