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Asymptotic normality and efficiency for certain goodness-of-fit tests
Uppsala University, Disciplinary Domain of Science and Technology, Faculty of Mathematics and Science.
1972 (English)In: Biometrika, ISSN 0006-3444, E-ISSN 1464-3510, Vol. 59, no 1, 137-145 p.Article in journal (Refereed) Published
Abstract [en]

Assume that a random sample of size n has been taken from a multinomial distribution with N cells. Let ξk be the number of observations in the kth cell and set

Zn=(ξ1, 1/N)+Fnn,N/N).

It is proved that, under general conditions, Zn is asymptotically normal when n and N tend to infinity so that n/N ↑ α > 0. This result is used to study asymptotic efficiency for certain goodness-of-fit tests. The chi-squared statistic turns out to be optimal in some situations.

Place, publisher, year, edition, pages
1972. Vol. 59, no 1, 137-145 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-180756DOI: 10.2307/2334624ISI: A1972M115400016OAI: oai:DiVA.org:uu-180756DiVA: diva2:552219
Available from: 2012-09-13 Created: 2012-09-10 Last updated: 2017-12-07Bibliographically approved

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