Statistics Colloquium : Dr. Martin Klein

Statistical Analysis of Noise Multiplied Data Using Multiple Imputation

Abstract : A statistical analysis of data that have been multiplied by randomly drawn noise variables in order to protect the confidentiality of individual
values has recently drawn some attention. If the distribution generating
the noise variables has low to moderate variance, then noise multiplied
data have been shown to yield accurate inferences in several typical
parametric models under a formal likelihood based analysis. However, the
likelihood based analysis is generally complicated due to the non-standard
and often complex nature of the distribution of the noise perturbed sample
even when the parent distribution is simple. This complexity places a
burden on data users who must either develop the required statistical
methods or implement the methods if already available or have access to
specialized software perhaps yet to be developed.  In this paper we
propose an alternate analysis of noise multiplied data based on multiple
imputation. Some advantages of this approach are that (1) the data user
can analyze the released data as if it were never perturbed, and (2) the
distribution of the noise variables does not need to be disclosed to the
data user.