publication . Preprint . 2018

Kernel Smoothing of the Treatment Effect CDF

Levy, Jonathan; van der Laan, Mark;
Open Access English
  • Published: 15 Nov 2018
Abstract
The strata-specific treatment effect or so-called blip for a randomly drawn strata of confounders defines a random variable and a corresponding cumulative distribution function. However, the CDF is not pathwise differentiable, necessitating a kernel smoothing approach to estimate it at a given point or perhaps many points. Assuming the CDF is continuous, we derive the efficient influence curve of the kernel smoothed version of the blip CDF and a CV-TMLE estimator. The estimator is asymptotically efficient under two conditions, one of which involves a second order remainder term which, in this case, shows us that knowledge of the treatment mechanism does not guar...
Subjects
free text keywords: Statistics - Methodology
Download from
20 references, page 1 of 2

Coyle, Jeremy et al. (2018). sl3. url: https://github.com/tlverse/sl3.

Dunn, Olive Jean (1961). \Multiple Comparisons Among Means". In: Journal of the American Statistical Association 56.293, pp. 52{64. [OpenAIRE]

Gill, Richard D and James M Robins (2001). \Causal inference for complex longitudinal data : the continuous case." In: Report Eurandom, Eindhoven: Eindhoven University of Technology 2001023.

Greenland, Sander and James Robins (1986). \Identi ability, Exchangeability, and Epidemiological Confounding". In: International Journal of Epidemiology 15.3.

van der Laan, Mark (2016). \A Generally E cient Targeted Minimum Loss Based Estimator". In: U.C. Berkeley Division of Biostatistics Working Paper Series 343. url: http://biostats.bepress.com/ ucbbiostat/paper343.

van der Laan, Mark and Susan Gruber (2016). \One-Step Targeted Minimum Loss-based Estimation Based on Universal Least Favorable One-Dimensional Submodels". In: The International Journal of Biostatistics 12(1), pp. 351{378.

van der Laan, Mark and Sherri Rose (2011). Targeted Learning. New York: Springer. [OpenAIRE]

van der Laan, Mark and Daniel Rubin (2006). \Targeted Maximum Likelihood Learning". In: U.C. Berkeley Division of Biostatistics Working Paper Series 213. url: http://biostats.bepress.com/ucbbiostat/ paper213.

Levy, Jonathan (2018a). \An Easy Implementation of CV-TMLE". In: arXiv:1811.04573 [stat.ME]. url: arxiv.org/abs/1811.04573.

| (2018b). blip CDF. url: https://github.com/jlstiles/blipCDF.

| (2018c). \Canonical Least Favorable Submodels: A New TMLE Procedure for Multidimensional Parameters". In: ArXiv e-prints. url: https://arxiv.org/abs/1811.01261.

Levy, Jonathan et al. (2018). \A Fundamental Measure of Treatment E ect Heterogeneity". In: arXiv:1811.03745 [stat.ME]. url: https://arxiv.org/abs/1811.03745.

Neyman, Jerzy (1923). \On the Application of Probability Theory to Agricultural Experiments. Essay on Principles. Section 9". In: Statistical Sciences 5.4. Translated and edited by D. M. Dabrowska and T. P. Speed from the Polish original which appeared in Roczniki Nauk Rolniczych Tom X, 1923, pp. 465{480.

Pearl, Judea (2000). Causality: Models, Reasoning and Inference. New York: Cambridge University Press, p. 484.

Riesz, Frgyes (1909). \Sur les operations fonctionnelles lineaires". In: C.R. Academy of Sciences Paris 149, pp. 974{977.

20 references, page 1 of 2
Abstract
The strata-specific treatment effect or so-called blip for a randomly drawn strata of confounders defines a random variable and a corresponding cumulative distribution function. However, the CDF is not pathwise differentiable, necessitating a kernel smoothing approach to estimate it at a given point or perhaps many points. Assuming the CDF is continuous, we derive the efficient influence curve of the kernel smoothed version of the blip CDF and a CV-TMLE estimator. The estimator is asymptotically efficient under two conditions, one of which involves a second order remainder term which, in this case, shows us that knowledge of the treatment mechanism does not guar...
Subjects
free text keywords: Statistics - Methodology
Download from
20 references, page 1 of 2

Coyle, Jeremy et al. (2018). sl3. url: https://github.com/tlverse/sl3.

Dunn, Olive Jean (1961). \Multiple Comparisons Among Means". In: Journal of the American Statistical Association 56.293, pp. 52{64. [OpenAIRE]

Gill, Richard D and James M Robins (2001). \Causal inference for complex longitudinal data : the continuous case." In: Report Eurandom, Eindhoven: Eindhoven University of Technology 2001023.

Greenland, Sander and James Robins (1986). \Identi ability, Exchangeability, and Epidemiological Confounding". In: International Journal of Epidemiology 15.3.

van der Laan, Mark (2016). \A Generally E cient Targeted Minimum Loss Based Estimator". In: U.C. Berkeley Division of Biostatistics Working Paper Series 343. url: http://biostats.bepress.com/ ucbbiostat/paper343.

van der Laan, Mark and Susan Gruber (2016). \One-Step Targeted Minimum Loss-based Estimation Based on Universal Least Favorable One-Dimensional Submodels". In: The International Journal of Biostatistics 12(1), pp. 351{378.

van der Laan, Mark and Sherri Rose (2011). Targeted Learning. New York: Springer. [OpenAIRE]

van der Laan, Mark and Daniel Rubin (2006). \Targeted Maximum Likelihood Learning". In: U.C. Berkeley Division of Biostatistics Working Paper Series 213. url: http://biostats.bepress.com/ucbbiostat/ paper213.

Levy, Jonathan (2018a). \An Easy Implementation of CV-TMLE". In: arXiv:1811.04573 [stat.ME]. url: arxiv.org/abs/1811.04573.

| (2018b). blip CDF. url: https://github.com/jlstiles/blipCDF.

| (2018c). \Canonical Least Favorable Submodels: A New TMLE Procedure for Multidimensional Parameters". In: ArXiv e-prints. url: https://arxiv.org/abs/1811.01261.

Levy, Jonathan et al. (2018). \A Fundamental Measure of Treatment E ect Heterogeneity". In: arXiv:1811.03745 [stat.ME]. url: https://arxiv.org/abs/1811.03745.

Neyman, Jerzy (1923). \On the Application of Probability Theory to Agricultural Experiments. Essay on Principles. Section 9". In: Statistical Sciences 5.4. Translated and edited by D. M. Dabrowska and T. P. Speed from the Polish original which appeared in Roczniki Nauk Rolniczych Tom X, 1923, pp. 465{480.

Pearl, Judea (2000). Causality: Models, Reasoning and Inference. New York: Cambridge University Press, p. 484.

Riesz, Frgyes (1909). \Sur les operations fonctionnelles lineaires". In: C.R. Academy of Sciences Paris 149, pp. 974{977.

20 references, page 1 of 2
Powered by OpenAIRE Research Graph
Any information missing or wrong?Report an Issue