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On Pooling of Data and Its Relative Efficiency

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  • Jinfeng Xu
  • Anthony Kuk

Abstract

type="main" xml:id="insr12070-abs-0001"> Pooling of data is often carried out to protect privacy or to save cost, with the claimed advantage that it does not lead to much loss of efficiency. We argue that this does not give the complete picture as the estimation of different parameters is affected to different degrees by pooling. We establish a ladder of efficiency loss for estimating the mean, variance, skewness and kurtosis, and more generally multivariate joint cumulants, in powers of the pool size. The asymptotic efficiency of the pooled data non-parametric/parametric maximum likelihood estimator relative to the corresponding unpooled data estimator is reduced by a factor equal to the pool size whenever the order of the cumulant to be estimated is increased by one. The implications of this result are demonstrated in case–control genetic association studies with interactions between genes. Our findings provide a guideline for the discriminate use of data pooling in practice and the assessment of its relative efficiency. As exact maximum likelihood estimates are difficult to obtain if the pool size is large, we address briefly how to obtain computationally efficient estimates from pooled data and suggest Gaussian estimation and non-parametric maximum likelihood as two feasible methods.

Suggested Citation

  • Jinfeng Xu & Anthony Kuk, 2015. "On Pooling of Data and Its Relative Efficiency," International Statistical Review, International Statistical Institute, vol. 83(2), pages 309-323, August.
    • Handle: RePEc:bla:istatr:v:83:y:2015:i:2:p:309-323
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    File URL: http://hdl.handle.net/10.1111/insr.12070
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    References listed on IDEAS

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    1. Martin Crowder, 2001. "On repeated measures analysis with misspecified covariance structure," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(1), pages 55-62.
    2. Kuk, Anthony Y. C. & Tan, C. C., 2009. "Estimating the Time-Varying Rate of Transmission of SARS in Singapore and Hong Kong Under Two Environments," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 88-96.
    3. Krishna Saha & Sudhir Paul, 2005. "Bias-Corrected Maximum Likelihood Estimator of the Negative Binomial Dispersion Parameter," Biometrics, The International Biometric Society, vol. 61(1), pages 179-185, March.
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