References
- Amato, U., and Antoniadis, A. (2001), “Adaptive Wavelet Series Estimation in Separable Nonparametric Regression Models,” Statistics and Computing, 11, 373–394.
- Barry, D. (1993), “Testing for Additivity of a Regression Function,” The Annals of Statistics, 21, 235–254.
- Biau, G. (2012), “Analysis of a Random Forests Model,” The Journal of Machine Learning Research, 98888, 1063–1095.
- Breiman, L. (1996), “Bagging Predictors,” Machine Learning, 24, 123–140.
- ——— (2001), “Random Forests,” Machine Learning, 45, 5–32.
- Buja, A., Hastie, T., and Tibshirani, R. (1989), “Linear Smoothers and Additive Models,” The Annals of Statistics, 17, 453–510.
- De Canditiis, D., and Sapatinas, T. (2004), “Testing for Additivity and Joint Effects in Multivariate Nonparametric Regression Using Fourier and Wavelet Methods,” Statistics and Computing, 14, 235–249.
- Derbort, S., Dette, H., and Munk, A. (2002), “A Test for Additivity in Nonparametric Regression,” Annals of the Institute of Statistical Mathematics, 54, 60–82.
- Dette, H., and Derbort, S. (2001), “Analysis of Variance in Nonparametric Regression Models,” Journal of Multivariate Analysis, 76, 110–137.
- Efron, B. (2014), “Estimation and Accuracy After Model Selection,” Journal of the American Statistical Association, 109, 991–1007.
- Eubank, R., Hart, J. D., Simpson, D., and Stefanski, L. A. (1995), “Testing for Additivity in Nonparametric Regression,” The Annals of Statistics, 23, 1896–1920.
- Fan, J., and Jiang, J. (2005), “Nonparametric Inferences for Additive Models,” Journal of the American Statistical Association, 100, 890–907.
- Friedman, J. H., and Stuetzle, W. (1981), “Projection Pursuit Regression,” Journal of the American Statistical Association, 76, 817–823.
- Hastie, T. J., and Tibshirani, R. J. (1990), Generalized Additive Models (Vol. 43), Boca Raton, FL: CRC Press.
- Hooker, G. (2004), “Discovering Additive Structure in Black Box Functions,” in Proceedings of the Tenth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, ACM, pp. 575–580.
- ——— (2007), “Generalized Functional ANOVA Diagnostics for High-Dimensional Functions of Dependent Variables,” Journal of Computational and Graphical Statistics, 16, 709–732.
- Johnson, W. B., and Lindenstrauss, J. (1984), “Extensions of Lipschitz Mappings Into a Hilbert Space,” Contemporary Mathematics, 26, 189–206.
- Linton, O. (1995), “A Kernel Method of Estimating Structured Nonparametric,” Biometrika, 82, 93–100.
- Lopes, M., Jacob, L., and Wainwright, M. J. (2011), “A More Powerful Two-Sample Test in High Dimensions Using Random Projection,” in Advances in Neural Information Processing Systems, pp. 1206–1214.
- Lou, Y., Caruana, R., Gehrke, J., and Hooker, G. (2013), “Accurate Intelligible Models With Pairwise Interactions,” in Proceedings of the 19th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, ACM, pp. 623–631.
- Mammen, E., Linton, O., and Nielsen, J. (1999), “The Existence and Asymptotic Properties of a Backfitting Projection Algorithm Under Weak Conditions,” The Annals of Statistics, 27, 1443–1490.
- Mentch, L., and Hooker, G. (2016), “Quantifying Uncertainty in Random Forests via Confidence Intervals and Hypothesis Tests,” Journal of Machine Learning Research, 17, 1–41.
- Opsomer, J. D., and Ruppert, D. (1998), “A Fully Automated Bandwidth Selection Method for Fitting Additive Models,” Journal of the American Statistical Association, 93, 605–619.
- ——— (1999), “A Root-n Consistent Backfitting Estimator for Semiparametric Additive Modeling,” Journal of Computational and Graphical Statistics, 8, 715–732.
- Scornet, E., Biau, G., and Vert, J.-P. (2015), “Consistency of Random Forests,” The Annals of Statistics, 43, 1716–1741.
- Sobol, I. M. (2001), “Global Sensitivity Indices for Nonlinear Mathematical Models and Their Monte Carlo Estimates,” Mathematics and Computers in Simulation, 55, 271–280.
- Srivastava, R., Li, P., and Ruppert, D. (2016), “RAPTT: An Exact Two-Sample Test in High Dimensions Using Random Projections,” Journal of Computational and Graphical Statistics, 25, 954–940.
- Stone, C. J. (1985), “Additive Regression and Other Nonparametric Models,” The Annals of Statistics, 13, 689–705.
- Wager, S., and Athey, S. (2015), “Estimation and Inference of Heterogeneous Treatment Effects Using Random Forests,” arXiv preprint arXiv:1510.04342.
- Wager, S., Hastie, T., and Efron, B. (2014), “Confidence Intervals for Random Forests: The Jackknife and the Infinitesimal Jackknife,” Journal of Machine Learning Research, 15, 1625–1651.