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

Ordinary rounding does not always satisfy a summation restriction on the rounding results. This can be resolved by applying multiplier methods, for which we present an easy-to-implement algorithm complemented by remarks on special families of multiplier methods, the arithmetic-mean and power-mean method, and a previously unaddressed family, the geometric-mean methods. Finally, several applications in statistics are pointed out, i.e. rounding percentages in descriptive statistics, rounding optimal designs of experiments, and rounding optimal sample allocations.