## Statistics Colloquium : Dr. Martin Klein

#### Census Bureau

Friday, March 1, 2019 · 11 AM - Noon

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.

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.