Rounding with multiplier methods: An efficient algorithm and applications in statistics (Q1290857)

The authors consider roundings for sums which satisfy prescribed summation restrictions such as percentages summing up to 100\%. For given weights \(w_1,\dots, w_c>0\) \((c\geq 2)\) and for some multiplier \(\nu\in (0,\infty)\) the expressions \(\nu w_i/\sum^c_{j=1} w_j\), \(i= 1,\dots, c\) are rounded appropriately to integers \(n_i\), \(i=1,\dots, c\) such that \(\sum^c_{i=1} n_i= n\) holds for some fixed positive integer \(n\). An iterative algorithm is presented which computes \(n_i\) in a finite number of steps. It is based on a sign-post sequence which is defined in the paper. Multiple solutions and special classes of multiplier rounding methods are discussed; some of the methods are applied to three fields in statistics.