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We present a general methodology for performing statistical inference on thecomponents of a real-valued matrix parameter for which rows and columns aresubject to order restrictions. The proposed estimation procedure is based on aniterative algorithm developed by Dykstra and Robertson (1982) for simple orderrestriction on rows and columns of a matrix. For any order restrictions on rowsand columns of a matrix, sufficient conditions are derived for the algorithm toconverge in a single application of row and column operations. The newalgorithm is applicable to a broad collection of order restrictions. Inpractice, it is easy to design a study such that the sufficient conditionsderived in this paper are satisfied. For instance, the sufficient conditionsare satisfied in a balanced design. Using the estimation procedure developed inthis article, a bootstrap test for order restrictions on rows and columns of amatrix is proposed. Computer simulations for ordinal data were performed tocompare the proposed test with some existing test procedures in terms of sizeand power. The new methodology is illustrated by applying it to a set ofordinal data obtained from a toxicological study.

Statistical inference under order restrictions on both rows and columns of a matrix, with an application in toxicology