Large-sample theory for parametric multiple imputation procedures

Wang, N

doi:10.1093/biomet/85.4.935

Cited by 154 publications

(213 citation statements)

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“…We should point out that this slight negative bias of Rubin's (1987) SD estimator is most likely due to the fact that the SD estimator based on the original data is itself slightly downward-biased. In the lognormal case, for the sample size n ¼ 100 of Table 2, we notice that Rubin's (1987) estimator is nearly unbiased for the true SD while Wang and Robins's (1998) estimators tend to overestimate the true SD more substantially. 6.…”

Section: Fully Noise-multiplied Datamentioning

confidence: 90%

“…With a larger sample size of n ¼ 500 (results not displayed here), we find that all standard deviation estimators have similar expectation; this statement is especially true for the normal case. With the sample size of n ¼ 100 we notice in Table 1 that the mean of Rubin's (1987) SD estimator is slightly less than the true SD while both of Wang and Robins's (1998) estimators have a mean slightly larger than the true SD. We should point out that this slight negative bias of Rubin's (1987) SD estimator is most likely due to the fact that the SD estimator based on the original data is itself slightly downward-biased.…”

Section: Fully Noise-multiplied Datamentioning

confidence: 95%

“…All results are obtained using the statistical computing software R (R Development Core Team 2011). UD: Analysis based on the unperturbed data y. NM10UIB: Analysis based on noise-multiplied data with h(r) defined by (5), e ¼ .10, and using the Type B imputation method and the associated combining rules of Wang and Robins (1998). NM10UIA1: Analysis based on noise-multiplied data with h(r) defined by (5), e ¼ .10, and using the Type A imputation method and Rubin's (1987) combining rules with the normal cut-off point for confidence interval construction.…”

Section: Simulation Study To Assess Accuracy Of Inferencementioning

confidence: 99%

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Statistical Analysis of Noise-Multiplied Data Using Multiple Imputation

Kampel¹,

Sinha²

2013

Journal of Official Statistics

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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 noisemultiplied 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 nonstandard 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 article 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.

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Section: Fully Noise-multiplied Datamentioning

confidence: 90%

Section: Fully Noise-multiplied Datamentioning

confidence: 95%

Section: Simulation Study To Assess Accuracy Of Inferencementioning

confidence: 99%

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Statistical Analysis of Noise-Multiplied Data Using Multiple Imputation

Kampel¹,

Sinha²

2013

Journal of Official Statistics

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“…Also, the variance estimator used in multiple imputation is not consistent for some estimated parameters. For examples, see Wang & Robins (1998) and Kim et al (2006).…”

Section: Introductionmentioning

confidence: 99%

“…One notable exception is Wang & Robins (1998) who studied the asymptotic properties of multiple imputation and a parametric frequentist imputation procedure. They considered the estimated parameterθ to be given, and did not discuss parameter estimation.…”

Section: Introductionmentioning

confidence: 99%

Parametric fractional imputation for missing data analysis

2011

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SUMMARYParametric fractional imputation is proposed as a general tool for missing data analysis. Using fractional weights, the observed likelihood can be approximated by the weighted mean of the imputed data likelihood. Computational efficiency can be achieved using the idea of importance sampling and calibration weighting. The proposed imputation method provides efficient parameter estimates for the model parameters specified in the imputation model and also provides reasonable estimates for parameters that are not part of the imputation model. Variance estimation is discussed and results from a limited simulation study are presented.

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Complex Surveys

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Large-sample theory for parametric multiple imputation procedures

Cited by 154 publications

References 16 publications

Statistical Analysis of Noise-Multiplied Data Using Multiple Imputation

Statistical Analysis of Noise-Multiplied Data Using Multiple Imputation

Parametric fractional imputation for missing data analysis

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