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Sensitivity analysis for inference with partially identifiable covariance matrices

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  • Max G’Sell
  • Shai Shen-Orr
  • Robert Tibshirani

Abstract

In some multivariate problems with missing data, pairs of variables exist that are never observed together. For example, some modern biological tools can produce data of this form. As a result of this structure, the covariance matrix is only partially identifiable, and point estimation requires that identifying assumptions be made. These assumptions can introduce an unknown and potentially large bias into the inference. This paper presents a method based on semidefinite programming for automatically quantifying this potential bias by computing the range of possible equal-likelihood inferred values for convex functions of the covariance matrix. We focus on the bias of missing value imputation via conditional expectation and show that our method can give an accurate assessment of the true error in cases where estimates based on sampling uncertainty alone are overly optimistic. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Max G’Sell & Shai Shen-Orr & Robert Tibshirani, 2014. "Sensitivity analysis for inference with partially identifiable covariance matrices," Computational Statistics, Springer, vol. 29(3), pages 529-546, June.
    • Handle: RePEc:spr:compst:v:29:y:2014:i:3:p:529-546
    DOI: 10.1007/s00180-013-0451-4
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    References listed on IDEAS

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    1. Rubin, Donald B, 1986. "Statistical Matching Using File Concatenation with Adjusted Weights and Multiple Imputations," Journal of Business & Economic Statistics, American Statistical Association, vol. 4(1), pages 87-94, January.
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    Cited by:

    1. Nickolay Trendafilov & Martin Kleinsteuber & Hui Zou, 2014. "Sparse matrices in data analysis," Computational Statistics, Springer, vol. 29(3), pages 403-405, June.

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