Covariate balancing based on kernel density estimates for controlled experiments

References

• Anderson, N. H., Hall, P., & Titterington, D. M. (1994). Two-sample test statistics for measuring discrepancies between two multivariate probability density functions using kernel-based density estimates. Journal of Multivariate Analysis, 50(1), 41–54. https://doi.org/10.1006/jmva.1994.1033
   Web of Science ®Google Scholar
• Bernstein, S. (1927). Sur l'extension du théorème limite du calcul des probabilités aux sommes de quantités dépendantes. Mathematische Annalen, 97(1), 1–59. https://doi.org/10.1007/BF01447859
   Google Scholar
• Bertsimas, D., Johnson, M., & Kallus, N. (2015). The power of optimization over randomization in designing experiments involving small samples. Operations Research, 63, 868–876. https://doi.org/10.1287/opre.2015.1361
   Web of Science ®Google Scholar
• Blackwell, M., Iacus, S., King, G., & Porro, G. (2009). cem: Coarsened exact matching in Stata. The Stata Journal, 9(4), 524–546. https://doi.org/10.1177/1536867X0900900402
   Web of Science ®Google Scholar
• de Lima, M. S., & G. S. Atuncar (2011). A Bayesian method to estimate the optimal bandwidth for multivariate kernel estimator. Journal of Nonparametric Statistics, 23(1), 137–148. https://doi.org/10.1080/10485252.2010.485200
   Web of Science ®Google Scholar
• Duong, T., & Hazelton, M. (2003). Plug-in bandwidth matrices for bivariate kernel density estimation. Journal of Nonparametric Statistics, 15(1), 17–30. https://doi.org/10.1080/10485250306039
   Web of Science ®Google Scholar
• Duong, T., & Hazelton, M. L. (2005). Cross-validation bandwidth matrices for multivariate kernel density estimation. Scandinavian Journal of Statistics, 32(3), 485–506. https://doi.org/10.1111/sjos.2005.32.issue-3
   Web of Science ®Google Scholar
• Efron, B., Hastie, T., Johnstone, I., & Tibshirani, R. (2004). Least angle regression. The Annals of Statistics, 32(2), 407–499. https://doi.org/10.1214/009053604000000067
   Web of Science ®Google Scholar
• Funk, M. J., Westreich, D., Wiesen, C., Stürmer, T., Brookhart, M. A., & Davidian, M. (2011). Doubly robust estimation of causal effects. American Journal of Epidemiology, 173(7), 761–767. https://doi.org/10.1093/aje/kwq439
   PubMed Web of Science ®Google Scholar
• Gurobi Optimization, LLC (2020). Gurobi optimizer reference manual.
   Google Scholar
• Härdle, W. K., Müller, M., Sperlich, S., & Werwatz, A. (2012). Nonparametric and semiparametric models. Springer Science & Business Media.
   Google Scholar
• Imbens, G. W., & Rubin, D. B. (2015). Causal inference for statistics, social, and biomedical sciences: An introduction. Cambridge University Press.
   Google Scholar
• Jones, M. C., Marron, J. S., & Sheather, S. J. (1996). Progress in data-based bandwidth selection for kernel density estimation. Computational Statistics, 11, 337–381.
   Web of Science ®Google Scholar
• Kallus, N. (2018). Optimal a priori balance in the design of controlled experiments. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 80(1), 85–112. https://doi.org/10.1111/rssb.12240
   Web of Science ®Google Scholar
• McHugh, R., & Matts, J. (1983). Post-stratification in the randomized clinical trial. Biometrics, 39(1), 217–225. https://doi.org/10.2307/2530821
   PubMed Web of Science ®Google Scholar
• Miller, B. L., & Goldberg, D. E. (1995). Genetic algorithms, tournament selection, and the effects of noise. Complex Systems, 9, 193–212.
   Google Scholar
• Morgan, K. L., & Rubin, D. B. (2012). Rerandomization to improve covariate balance in experiments. The Annals of Statistics, 40(2), 1263–1282. https://doi.org/10.1214/12-AOS1008
   Web of Science ®Google Scholar
• Morgan, K. L., & Rubin, D. B. (2015). Rerandomization to balance tiers of covariates. Journal of the American Statistical Association, 110(512), 1412–1421. https://doi.org/10.1080/01621459.2015.1079528
   PubMed Web of Science ®Google Scholar
• Pearl, J. (2000). Causality: Models, reasoning, and inference. Cambridge University Press.
   Google Scholar
• Rosenbaum, P. (2017). Observation and experiment: An introduction to causal inference. Harvard University Press.
   Google Scholar
• Rosenbaum, P. R., & Rubin, D. B. (1983). The central role of the propensity score in observational studies for causal effects. Biometrika, 70, 41–55. https://doi.org/10.1093/biomet/70.1.41
   Web of Science ®Google Scholar
• Rubin, D. B. (1980). Randomization analysis of experimental data: The Fisher randomization test comment. Journal of the American Statistical Association, 75, 591–593.
   Web of Science ®Google Scholar
• Rubin, D. B. (2005). Causal inference using potential outcomes: Design, modeling, decisions. Journal of the American Statistical Association, 100(469), 322–331. https://doi.org/10.1198/016214504000001880
   Web of Science ®Google Scholar
• Sain, S. R., Baggerly, K. A., & Scott, D. W. (1994). Cross-validation of multivariate densities. Journal of the American Statistical Association, 89(427), 807–817. https://doi.org/10.1080/01621459.1994.10476814
   Web of Science ®Google Scholar
• Scott, D. W. (2015). Multivariate density estimation: Theory, practice, and visualization. Wiley.
   Google Scholar
• Sheather, S. J., & Jones, M. C. (1991). A reliable data-based bandwidth selection method for kernel density estimation. Journal of the Royal Statistical Society. Series B (Methodological), 53(3), 683–690. https://doi.org/10.1111/rssb.1991.53.issue-3
   Web of Science ®Google Scholar
• Silverman, B. W. (1986). Density estimation for statistics and data analysis, vol. CRC Press.
   Google Scholar
• Simonoff, J. S. (2012). Smoothing methods in statistics. Springer Science & Business Media.
   Google Scholar
• Van Laarhoven, P. J., & Aarts, E. H. (1987). Simulated annealing. In Simulated annealing: Theory and applications (pp. 7–15). Springer.
   Google Scholar
• Wand, M. P., & Jones, M. C. (1993). Comparison of smoothing parameterizations in bivariate kernel density estimation. Journal of the American Statistical Association, 88(422), 520–528. https://doi.org/10.1080/01621459.1993.10476303
   Web of Science ®Google Scholar
• Wand, M. P., & Jones, M. C. (1994). Multivariate plug-in bandwidth selection. Computational Statistics, 9, 97–116.
   Web of Science ®Google Scholar
• Wu, C. J., & Hamada, M. S. (2011). Experiments: planning, analysis, and optimization, vol. Wiley.
   Google Scholar
• Xie, H., & Aurisset, J. (2016). Improving the sensitivity of online controlled experiments: Case studies at netflix. In Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (pp. 645–654). ACM.
   Google Scholar
• Zhang, X., King, M. L., & Hyndman, R. J. (2006). A Bayesian approach to bandwidth selection for multivariate kernel density estimation. Computational Statistics & Data Analysis, 50(11), 3009–3031. https://doi.org/10.1016/j.csda.2005.06.019
   Web of Science ®Google Scholar