A note on constructive procedure for unbiased controlled rounding

The technique of controlled rounding is to replace each entry of an array by an adjacent integer multiple of the rounding base, preserving the additive structure of the array. The controlled rounding is said to be zero-restricted, if it also satisfies the condition that the values which are already the integer multiples of the base, remain unchanged. The main purpose of controlled rounding is to ensure confidentiality of aggregate statistics. Notable amongst the various authors, who have thoroughly discussed the problem of controlled rounding, are Nargundkar and Saveland (1972), Dalenius (1981), Ernst (1981), Cox and Ernst (1982), Causey, Cox and Ernst (1985) and Cox (1987). In a recent work on controlled rounding, Cox (1987) has developed a procedure for unbiased controlled rounding in two dimensions. The purpose of this note is to improve upon the procedure of Cox (1987), so that it terminates in fewer steps. The example in the case of two-way statistical table, solved by Cox (1987), has been reconsidered to highlight the utility of the proposed procedure.