Symmetrically distributed and unbiased estimators in linear models
- 1 January 1982
- journal article
- research article
- Published by Taylor & Francis in Communications in Statistics - Theory and Methods
- Vol. 11 (7) , 721-729
- https://doi.org/10.1080/03610928208828266
Abstract
Let Y be distributed symmetrically about Xβ. Natural generalizations of odd location statistics, say T‘Y’, and even location-free statistics, say W‘Y’, that were used by Hogg ‘1960, 1967)’ are introduced. We show that T‘Y’ is distributed symmetrically about β and thus E[T‘Y’] = β and that each element of T‘Y’ is uncorrelated with each element of W‘Y’. Applications of this result are made to R-estiraators and the result is extended to a multivariate linear model situation.Keywords
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