The International Journal of Biostatistics
Ed. by Chambaz, Antoine / Hubbard, Alan E. / van der Laan, Mark J.
2 Issues per year
IMPACT FACTOR 2014: 0.741
5-year IMPACT FACTOR: 1.475
SCImago Journal Rank (SJR): 1.039
Source Normalized Impact per Paper (SNIP): 0.746
Mathematical Citation Quotient 2013: 0.04
Volume 11 (2015)
Volume 7 (2011)
Volume 5 (2009)
Volume 4 (2008)
Volume 3 (2007)
Volume 2 (2006)
Volume 1 (2005)
Most Downloaded Articles
- An Introduction to Causal Inference by Pearl, Judea
- Sample Size Estimation for Repeated Measures Analysis in Randomized Clinical Trials with Missing Data by Lu, Kaifeng/ Luo, Xiaohui and Chen, Pei-Yun
- Survival Models in Health Economic Evaluations: Balancing Fit and Parsimony to Improve Prediction by Jackson, Christopher H/ Sharples, Linda D and Thompson, Simon G
- Accuracy of Conventional and Marginal Structural Cox Model Estimators: A Simulation Study by Xiao, Yongling/ Abrahamowicz, Michal and Moodie, Erica E. M.
- Evaluating treatment effectiveness in patient subgroups: a comparison of propensity score methods with an automated matching approach by Radice, Rosalba/ Ramsahai, Roland/ Grieve, Richard/ Kreif, Noemi/ Sadique, Zia and Sekhon, Jasjeet S.
Targeted Maximum Likelihood Learning
1Division of Biostatistics, School of Public Health, University of California, Berkeley
2University of California, Berkeley
Citation Information: The International Journal of Biostatistics. Volume 2, Issue 1, ISSN (Online) 1557-4679, DOI: 10.2202/1557-4679.1043, December 2006
- Published Online:
Suppose one observes a sample of independent and identically distributed observations from a particular data generating distribution. Suppose that one is concerned with estimation of a particular pathwise differentiable Euclidean parameter. A substitution estimator evaluating the parameter of a given likelihood based density estimator is typically too biased and might not even converge at the parametric rate: that is, the density estimator was targeted to be a good estimator of the density and might therefore result in a poor estimator of a particular smooth functional of the density. In this article we propose a one step (and, by iteration, k-th step) targeted maximum likelihood density estimator which involves 1) creating a hardest parametric submodel with parameter epsilon through the given density estimator with score equal to the efficient influence curve of the pathwise differentiable parameter at the density estimator, 2) estimating epsilon with the maximum likelihood estimator, and 3) defining a new density estimator as the corresponding update of the original density estimator. We show that iteration of this algorithm results in a targeted maximum likelihood density estimator which solves the efficient influence curve estimating equation and thereby yields a locally efficient estimator of the parameter of interest, under regularity conditions. In particular, we show that, if the parameter is linear and the model is convex, then the targeted maximum likelihood estimator is often achieved in the first step, and it results in a locally efficient estimator at an arbitrary (e.g., heavily misspecified) starting density.We also show that the targeted maximum likelihood estimators are now in full agreement with the locally efficient estimating function methodology as presented in Robins and Rotnitzky (1992) and van der Laan and Robins (2003), creating, in particular, algebraic equivalence between the double robust locally efficient estimators using the targeted maximum likelihood estimators as an estimate of its nuisance parameters, and targeted maximum likelihood estimators. In addition, it is argued that the targeted MLE has various advantages relative to the current estimating function based approach. We proceed by providing data driven methodologies to select the initial density estimator for the targeted MLE, thereby providing data adaptive targeted maximum likelihood estimation methodology. We illustrate the method with various worked out examples.
Keywords: causal effect; cross-validation; efficient influence curve; estimating function; locally efficient estimation; loss function; maximum likelihood estimation; sieve; targeted maximum likelihood estimation; variable importance
Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.