Statistical Analysis of Noise-Multiplied Data Using Multiple Imputation

Kampel, Martin; Sinha, Bimal K.

doi:10.2478/jos-2013-0034

Cited by 6 publications

(2 citation statements)

References 21 publications

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“…For some standard results on Wishart distribution which will be used throughout this paper, we refer to Anderson (2003) and Muirhead (1982). Some additional relevant references in this context are Klein and Sinha (2013), Klein, Zylstra and Sinha (2019) and Moura et al (2021).…”

Section: Introductionmentioning

confidence: 99%

Bayesian Analysis of Singly Imputed Synthetic Data under the Multivariate Normal Model

Guin,

Roy,

Sinha

2023

Int. J. of Stat. Sci.

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We develop appropriate Bayesian procedures to draw inference about the parameters under a multivariate normal model based on synthetic data. We consider two standard forms of synthetic data, generated under plug in sampling method and posterior predictive sampling method. In addition to point estimates of the mean vector and dispersion matrix, Bayesian credible sets for the mean vector and the generalized variance are also provided under both the scenarios. The analysis in the case when some (partial) features are sensitive and need to be hidden is also briey indicated. Vol. 23(2), November, 2023, pp 1-18

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Section: Introductionmentioning

confidence: 99%

Bayesian Analysis of Singly Imputed Synthetic Data under the Multivariate Normal Model

Guin,

Roy,

Sinha

2023

Int. J. of Stat. Sci.

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“…While evaluation of disclosure risk when releasing any kind of perturbed data is essential, there is no unique way to exactly quantify it or even define it. Reiter [33], Reiter and Mitra [34], Klein and Sinha [19] and others have attempted it earlier with their own approaches and understandings. In this section we take the following premise.…”

Section: Disclosure Risk Evaluationmentioning

confidence: 99%

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

Kampel

Mathew

Sinha

2014

JPC

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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.

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Density Approximant Based on Noise Multiplied Data

Lin

2014

Lecture Notes in Computer Science

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Using noise multiplied data to protect confidential data has recently drawn some attention. Understanding the probability property of the underlying confidential data based on their masked data is of interest in confidential data analysis. This paper proposes the approach of sample-moment-based density approximant based on noise multiplied data and provides a new manner for approximating the density function of the underlying confidential data without accessing the original data. The approach of sample-moment-based density approximant is an extension of the approach of moment-based density approximant, which is mathematically equivalent to traditional orthogonal polynomials ap-proaches to the probability density function (Provost, 2005). This paper shows that, regardless of a negligible probability, a moment-based density approximant can be well approximated by its sample-moment-based approximant if the size of the sample used in the evaluation is reasonable large. Consequently, a density function can be reasonably approximated by its sample-moment-based density approximant. This paper focuses on the properties and the performance of the approach of the sample-moment-based density approximant based on noise multiplied data. Due to the restriction on the number of pages, some technical issues on implementing the approach proposed in practice will be discussed in another paper. Abstract. Using noise multiplied data to protect confidential data has recently drawn some attention. Understanding the probability property of the underlying confidential data based on their masked data is of interest in confidential data analysis. This paper proposes the approach of sample-moment-based density approximant based on noise multiplied data and provides a new manner for approximating the density function of the underlying confidential data without accessing the original data.The approach of sample-moment-based density approximant is an extension of the approach of moment-based density approximant, which is mathematically equivalent to traditional orthogonal polynomials approaches to the probability density function (Provost, 2005). This paper shows that, regardless of a negligible probability, a moment-based density approximant can be well approximated by its sample-moment-based approximant if the size of the sample used in the evaluation is reasonable large. Consequently, a density function can be reasonably approximated by its sample-moment-based density approximant. This paper focuses on the properties and the performance of the approach of the sample-moment-based density approximant based on noise multiplied data. Due to the restriction on the number of pages, some technical issues on implementing the approach proposed in practice will be discussed in another paper.

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Statistical Analysis of Noise-Multiplied Data Using Multiple Imputation

Cited by 6 publications

References 21 publications

Bayesian Analysis of Singly Imputed Synthetic Data under the Multivariate Normal Model

Bayesian Analysis of Singly Imputed Synthetic Data under the Multivariate Normal Model

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

Density Approximant Based on Noise Multiplied Data

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