For a fixed probability $0 < \gamma < 1$, the "most outlying" $100(1 - \gamma){\tt\%}$ subset of the data from a location model may be located with a Grubbs outlier subset test statistic. This subset is essentially located in terms of its complement, which is the connected $100\gamma{\tt\%}$ span of the data which supports the smallest sample variance. We show that this range of the data may be characterized approximately as the $100\gamma{\tt\%}$ span such that its midpoint is equal to the trimmed mean averaged over the span. Such a range forms a tolerance interval for predicting a future observation from the location model, and the asymptotic laws for its location, coverage, and center are presented.
@article{1176345702,
author = {Butler, Ronald W.},
title = {Nonparametric Interval and Point Prediction Using Data Trimmed by a Grubbs-Type Outlier Rule},
journal = {Ann. Statist.},
volume = {10},
number = {1},
year = {1982},
pages = { 197-204},
language = {en},
url = {http://dml.mathdoc.fr/item/1176345702}
}
Butler, Ronald W. Nonparametric Interval and Point Prediction Using Data Trimmed by a Grubbs-Type Outlier Rule. Ann. Statist., Tome 10 (1982) no. 1, pp. 197-204. http://gdmltest.u-ga.fr/item/1176345702/