The Spiking Problem in the Context of the Isotonic Regression

The usual estimators of the regression under isotonicity are known to present the so-called spiking problem, that is, they are very sensitive at the tails. Three design-based strategies in order to alleviate this effect are discussed. The proposed strategies will provide uniform consistency on the (closed and bounded) working interval. Firstly, the usual isotonic regression with a suitable number of observations at the edges of the interval is considered. Secondly, a reallocation of part of the edge observations at some artificial adjacent points is suggested. Finally, a strategy based on constraining the isotonic regression to take values within some horizontal bands is investigated. Simulation studies illustrate the performance of the proposed estimators in practice.