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Prediction and calibration for multiple correlated variables

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  • Bhaumik, Dulal K.
  • Nordgren, Rachel K.

Abstract

The standard approach for prediction of multiple correlated outcome measures overpredicts the unknown observation in the linear model setup if associated covariate measures follow a certain distribution. It is desired to have a nonempty confidence region when some covariate measures are missing and required to be estimated. This article develops a methodology for prediction and proposes a shrinkage predictor with a smaller risk compared to the one based on the maximum likelihood estimate. It also provides an algorithm for constructing a nonempty confidence region for unknown covariates. Proposed methodology is shown to perform well in terms of maintaining a smaller risk in prediction and the coverage probability in calibration. Results are illustrated with a recent behavioral science dataset.

Suggested Citation

  • Bhaumik, Dulal K. & Nordgren, Rachel K., 2019. "Prediction and calibration for multiple correlated variables," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 313-327.
    • Handle: RePEc:eee:jmvana:v:173:y:2019:i:c:p:313-327
    DOI: 10.1016/j.jmva.2019.03.001
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    References listed on IDEAS

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    1. Dunkler, Daniela & Sauerbrei, Willi & Heinze, Georg, 2016. "Global, Parameterwise and Joint Shrinkage Factor Estimation," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 69(i08).
    2. Leo Breiman & Jerome H. Friedman, 1997. "Predicting Multivariate Responses in Multiple Linear Regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(1), pages 3-54.
    3. Lynn R. LaMotte & Jeffrey D. Wells, 2016. "Inverse prediction for multivariate mixed models with standard software," Statistical Papers, Springer, vol. 57(4), pages 929-938, December.
    4. Wei, Wei & Balabdaoui, Fadoua & Held, Leonhard, 2017. "Calibration tests for multivariate Gaussian forecasts," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 216-233.
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