Likelihood Based Inference Under Noise Multiplication

When statistical agencies release microdata to the public, a major concern is the control of disclosure risk, while ensuring utility in the released data. Often some statistical disclosure control methods such as data swapping, multiple imputation, top coding, and perturbation with random noise, are applied before releasing the data. This article develops methodology for data analysis when each original observation is multiplied by random noise for the purpose of statistical disclosure control. A parametric model is assumed, and specific details are provided for the exponential, normal and lognormal models. Our analysis shows that noise multiplied data can yield accurate inferences, and detailed simulation results provide guidance as to how the dispersion of the noise generating distribution affects accuracy of the inference.