Using the Lehmer Mean to Assess Business Data Protection: Statistical Disclosure Control and the Truncated Moment Problem

Confidential business data needs protection against disclosure. Often this data is protected by releasing sample means, variances and higher power moments. Motivated by statistical disclosure control obligations and the need to publish business data safely, we explain how calculating the Lehmer mean from released power moments can lead to the unwanted disclosure of the largest data value. We explain how similar disclosure can apply to smaller data values and provide an approximate solution to the Truncated Moment Problem. We briefly discuss the Gini mean and the relationship between sample central and raw moments.