Abstract
The L 1 estimate for the p-variable linear model has the well known property of fitting p observations exactly. A less well known property is that certain subsets of p observations will not be fit by the L 1 estimate for any realization of the dependent variables. This property is shown to generalize to other regression quantiles and to the set of all regression quantiles. This identifies subsets of the data which seem to be unimportant. The analog of the property for the location submodel is a situation where one observation, say the first, would not be any quantile for any sample. The implications of the property for other estimates which are based on p-observation subsets are discussed, but the property is considered mainly because it seems strange.
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