Nonparametric Interval and Point Prediction Using Data Trimmed by a Grubbs-Type Outlier Rule

Abstract

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.