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Super Learner Based Conditional Density Estimation with Application to Marginal Structural Models

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  • Díaz Muñoz Iván

    (University of California, Berkeley)

  • van der Laan Mark J.

    (University of California, Berkeley)

Abstract

In this paper, we present a histogram-like estimator of a conditional density that uses cross-validation to estimate the histogram probabilities, as well as the optimal number and position of the bins. This estimator is an alternative to kernel density estimators when the dimension of the covariate vector is large. We demonstrate its applicability to estimation of Marginal Structural Model (MSM) parameters in which an initial estimator of the exposure mechanism is needed. MSM estimation based on the proposed density estimator results in less biased estimates, when compared to estimates based on a misspecified parametric model.

Suggested Citation

  • Díaz Muñoz Iván & van der Laan Mark J., 2011. "Super Learner Based Conditional Density Estimation with Application to Marginal Structural Models," The International Journal of Biostatistics, De Gruyter, vol. 7(1), pages 1-20, October.
    • Handle: RePEc:bpj:ijbist:v:7:y:2011:i:1:n:38
    DOI: 10.2202/1557-4679.1356
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    References listed on IDEAS

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    1. van der Laan Mark J. & Dudoit Sandrine & Keles Sunduz, 2004. "Asymptotic Optimality of Likelihood-Based Cross-Validation," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 3(1), pages 1-25, March.
    2. van der Laan Mark J. & Rubin Daniel, 2006. "Targeted Maximum Likelihood Learning," The International Journal of Biostatistics, De Gruyter, vol. 2(1), pages 1-40, December.
    3. Vaart Aad W. van der & Dudoit Sandrine & Laan Mark J. van der, 2006. "Oracle inequalities for multi-fold cross validation," Statistics & Risk Modeling, De Gruyter, vol. 24(3), pages 1-21, December.
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    Cited by:

    1. Ted Westling & Peter Gilbert & Marco Carone, 2020. "Causal isotonic regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(3), pages 719-747, July.
    2. Iván Díaz & Alan Hubbard & Anna Decker & Mitchell Cohen, 2015. "Variable Importance and Prediction Methods for Longitudinal Problems with Missing Variables," PLOS ONE, Public Library of Science, vol. 10(3), pages 1-17, March.
    3. Rachael V. Phillips & Mark J. van der Laan, 2022. "Rachael V. Phillips and Mark J. van der Laan’s contribution to the Discussion of ‘Assumption‐lean inference for generalised linear model parameters’ by Vansteelandt and Dukes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(3), pages 717-718, July.
    4. Jacqueline A. Mauro & Edward H. Kennedy & Daniel Nagin, 2020. "Instrumental variable methods using dynamic interventions," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(4), pages 1523-1551, October.
    5. Iván Díaz Muñoz & Mark van der Laan, 2012. "Population Intervention Causal Effects Based on Stochastic Interventions," Biometrics, The International Biometric Society, vol. 68(2), pages 541-549, June.

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