The L 1 Solution Set in Two - Way Tables

techniqlle of1eastabsolllt~id~viationsa..l) is investigated in twQ-way tables. The.• characterization.ofthe(oftennon-unique)LlSOllltions~tintwo-\Vay tables given by Kemperman (1984) and the graph inSiegel (1983) are exploited to prove several results. When all cells have an odd number of replicates, unique non-degenerate Ll solutions are possible only when the factor with fewer levels has an odd number of levels. When all cells have an even number of replicates, unique non-degenerate L1 solutions are not possible. The highest dimension that an L1 solution set may have for a particular table is also found. Through simulation it was discovered that the vertex of the Ll solution set that minimizes the sum of squares follows the asymptotic normal approximation somewhat better than the usualL1 S6Iu~()ninS~ltabl~S ..•• ~lleasYll1Ptotisappro~IIlationis nOtvery good for either solution when the errors are long tailed. Simulations also revealed that the L1 solution set is often surprisingly large for two-way tables. Some discussion of the general regression problem is also. given.