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Tests Based on Linear Combinations of the Orthogonal Components of the Cramer-von Mises Statistic When Parameters are Estimated

David Schoenfeld
The Annals of Statistics
Vol. 8, No. 5 (Sep., 1980), pp. 1017-1022
Stable URL: http://www.jstor.org/stable/2240432
Page Count: 6
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Tests Based on Linear Combinations of the Orthogonal Components of the Cramer-von Mises Statistic When Parameters are Estimated
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Abstract

In a previous work, the author showed how linear combinations of the orthogonal components of the Cramer-von Mises statistic could be used to test fit to a fully specified distribution function. In this paper, the results are extended to the case where r parameters are estimated from the data. It is shown that if the coefficient vector of the linear combination is orthogonal to a specified r dimensional subspace, then the asymptotic distribution of that combination is the same whether the parameters are estimated or known exactly.

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