Noise Multiplication for Statistical Disclosure Control of Extreme Values in Log-normal Regression Samples

Abstract

In this article multiplication of original data values by random noise is suggested as a disclosure control strategy when only the top part of the data is sensitive, as is often the case with income data. The proposed method can serve as an alternative to top coding which is a standard method in this context. Because the log-normal distribution usually fits income data well, the present investigation focuses exclusively on the log-normal. It is assumed that the log-scale mean of the sensitive variable is described by a linear regression on a set of non-sensitive covariates, and we show how a data user can draw valid inference on the parameters of the regression. An appealing feature of noise multiplication is the presence of an explicit tuning mechanism, namely, the noise generating distribution. By appropriately choosing this distribution, one can control the accuracy of inferences and the level of disclosure protection desired in the released data. Usually, more information is retained on the top part of the data under noise multiplication than under top coding. Likelihood based analysis is developed when only the large values in the data set are noise multiplied, under the assumption that the original data form a sample from a log-normal distribution. In this scenario, data analysis methods are developed under two types of data releases: (I) each released value includes an indicator of whether or not it has been noise multiplied, and (II) no such indicator is provided. A simulation study is carried out to assess the accuracy of inference for some parameters of interest. Since top coding and synthetic data methods are already available as disclosure control strategies for extreme values, some comparisons with the proposed method are made through a simulation study. The results are illustrated with a data analysis example based on 2000 U.S. Current Population Survey data. Furthermore, a disclosure risk evaluation of the proposed methodology is presented in the context of the Current Population Survey data example, and the disclosure risk of the proposed noise multiplication method is compared with the disclosure risk of synthetic data.

Likelihood Based Finite Sample Inference for Singly Imputed Synthetic Data Under the Multivariate Normal and Multiple Linear Regression Models

“…The above criterion was also used by Klein et al (2014) to measure the level of privacy protection in the context of noise multiplication to protect extreme values, and it is similar to a criterion used by Lin and Wise (2012). Notice that if the probability (23) is small, then we would conclude that there is a high level of protection against disclosure; and if this probability is large, then we would conclude that there is a low level of protection against disclosure.…”

“…In Subsection 6.2 we compare the disclosure risk of singly imputed partially synthetic data with that of multiply imputed partially synthetic data in the context of this CPS data example. These CPS data were previously used by Drechsler and Reiter (2010) and Reiter (2005a;c) for illustrating aspects of synthetic data methodology, and by Klein et al (2014) for illustrating methodology of noise multiplication for statistical disclosure control. While the entire data file contains household, family, and individual records, we focus only on the household records, as did Drechsler and Reiter (2010), Reiter (2005a;c), and Klein et al (2014).…”

“…In the notation of Section 4, we let the response variable y be the natural logarithm of household income. A number of covariates are available on the data file, and for the illustration presented here we use the same set of covariates as in Klein et al (2014) We refer to the Current Population Survey March 2000 technical documentation (available at http://www.census.gov/prod/techdoc/cps/cpsmar00.pdf) and Klein et al (2014) for details. Therefore x, the vector of regressor variables, is defined as…”

A New Algorithm for Protecting Aggregate Business Microdata via a Remote System

“…It is not necessary for the realization ofŶ 1 to be exactly equal to y 1 -the degree of accuracy required for disclosure must be determined by the statistical agency. The following definition of disclosure risk we adopt is similar to that used by Lin and Wise (2012) and Klein et al(2014).…”

“…Typically, some industries will be dominated by large businesses whose information is difficult to conceal by existing data masking methods. Non-perturbative data masking, such as top coding (Klein et al 2014), suppression (Salazar-González 2005) and micro-aggregation (Defays and Nanopoulos 1993), significantly reduce information of continuous data items such as turnover or profit, which are of key interest to data users. Perturbation methods, such as data swapping (Moore 1996), synthetic data (Rubin 1993) and noise addition (Kim and Winkler 1995), cannot efficiently protect businesses with distinct continuous-valued characteristics.…”