Statistical Properties of Multiplicative Noise Masking for Confidentiality Protection
Tapan K. Nayak, Bimal Sinha, Laura Zayatz
This article investigates statistical properties of random noise multiplication as a data masking procedure, especially for tabular magnitude data. It is shown that (i) the original data moments and correlations can be unbiasedly recovered from noise multiplied data (ii) for both finite and infinite population sampling, all polynomial estimators for the original data can be adopted easily for the masked data and (iii) for tabular magnitude data, multiplicative noises affect the quality of a cell total more for sensitive cells than for nonsensitive cells. Disclosure risk assessment and the choice of the noise distribution are discussed using the prediction error variance in a conservative scenario, where an intruder knows the perturbed cell total and all values within the cell, except the target units value. We also derive some interesting properties of a balanced noise method, and ascertain the reduction in the variance of a cell total by using the balancing mechanism.
Data quality, disclosure risk, noise variance, tabular data, unbiasedness, variance inflation