Least squares and least absolute deviation procedures in approximately linear models

摘要: Abstract The Approximately Linear Model, introduced by Sacks and Ylvisaker (1978, Annals of Statistics), represents deviations from the ideal linear model y = Xβ + e, considering b where is an unknown bias vector whose components are bounded in absolute value, i.e., |bi| ⩽ ri, ri being a known nonnegative number. We propose to estimate β minimizing maximum weighted sum squared deviations, or computed subject ri. In former case criterion be minimized turns out combination least squares deviation criteria for model. obtained latter approach (i.e., deviations) independent assumed bound on bi. This establishes another robustness property criterion.