References
- Aguilera, N., Forzani, L., and Morin, P. (2011), “On Uniform Consistent Estimators for Convex Regression,” Journal of Nonparametric Statistics, 23, 897–908.
- Allon, G., Beenstock, M., Hackman, S., Passy, U., and Shapiro, A. (2007), “Nonparametric Estimation of Concave Production Technologies by Entropic Methods,” Journal of Applied Econometrics, 22, 795–816.
- Aybat, N. S., and Iyengar, G. (2012), “A First-Order Augmented Lagrangian Method for Compressed Sensing,” SIAM Journal on Optimization, 22, 429–459.
- Aybat, N. S., and Wang, Z. (2014), “A Parallel Method for Large Scale Convex Regression Problems,” in Proceeding of the IEEE 53rd Annual Conference on Decision and Control, pp. 5710–5717.
- Ayer, M., Brunk, H. D., Ewing, G. M., Reid, W. T., and Silverman, E. (1955), “An Empirical Distribution Function for Sampling with Incomplete Information,” Annals of Mathematical Statistics, 26, 641–647.
- Balabdaoui, F. (2007), “Consistent Estimation of a Convex Density at the Origin,” Mathematical Methods of Statistics, 16, 77–95.
- Balázs, G., György, A., and Szepesvári, C. (2015), “Near-Optimal Max-Affine Estimators for Convex Regression,” in Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics, pp. 56–64.
- Bertsekas, D. P. (1999), Nonlinear Programming (2nd ed.), Belmont, MA: Athena Scientific.
- Birke, M., and Dette, H. (2007), “Estimating a Convex Function in Nonparametric Regression,” Scandinavian Journal of Statistics, 34, 384–404.
- Boyd, S., Parikh, N., Chu, E., Peleato, B., and Eckstein, J. (2011), “Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers,” Foundations and Trends® in Machine Learning, 3, 1–122.
- Boyd, S., and Vandenberghe, L. (2004), Convex Optimization, Cambridge, UK: Cambridge University Press.
- Brunk, H. D. (1955), “Maximum Likelihood Estimates of Monotone Parameters,” Annals of Mathematical Statistics, 26, 607–616.
- Chen, C., He, B., Ye, Y., and Yuan, X. (2016), “The Direct Extension of ADMM for Multi-Block Convex Minimization Problems is Not Necessarily Convergent,” Mathematical Programming, 155, 57–79.
- Cule, M., Samworth, R., and Stewart, M. (2010), “Maximum Likelihood Estimation of a Multi-Dimensional Log-Concave Density,” Journal of the Royal Statistical Society, Series B, 72, 545–607.
- Du, P., Parmeter, C. F., and Racine, J. S. (2013), “Nonparametric Kernel Regression With Multiple Predictors and Multiple Shape Constraints,” Statistica Sinica, 23, 1347–1371.
- Hannah, L. A., and Dunson, D. B. (2013), “Multivariate Convex Regression With Adaptive Partitioning,” Journal of Machine Learning Research, 14, 3261–3294.
- Hastie, T., Tibshirani, R., and Friedman, J. (2009), The Elements of Statistical Learning: Data Mining, Inference, and Prediction (2nd ed.), Springer Series in Statistics, New York: Springer.
- Hong, M., and Luo, Z.-Q. (2017), “On the Linear Convergence of the Alternating Direction Method of Multipliers,” Mathematical Programming, 162, 165–199.
- Kuosmanen, T. (2008), “Representation Theorem for Convex Nonparametric Least Squares,” The Econometrics Journal, 11, 308–325.
- Lim, E. (2014), “On Convergence Rates of Convex Regression in Multiple Dimensions,” INFORMS Journal on Computing, 26, 616–628.
- Lim, E., and Glynn, P. W. (2012), “Consistency of Multidimensional Convex Regression,” Operations Research, 60, 196–208.
- Mammen, E. (1991), “Estimating a Smooth Monotone Regression Function,” Annals of Statistics, 19, 724–740.
- Matzkin, R. L. (1994), “Restrictions of Economic Theory in Nonparametric Methods,” Handbook of Econometrics, 4, 2523–2558.
- Mekaroonreung, M., and Johnson, A. L. (2012), “Estimating the Shadow Prices of SO2 and NOx for US Coal Power Plants: A Convex Nonparametric Least Squares Approach,” Energy Economics, 34, 723–732.
- Meyer, R. F., and Pratt, J. W. (1968), “The Consistent Assessment and Fairing of Preference Functions,” IEEE Transactions on Systems Science and Cybernetics, 4, 270–278.
- Michelot, C. (1986), “A Finite Algorithm for Finding the Projection of a Point Onto the Canonical Simplex of Rn,” Journal of Optimization Theory and Applications, 50, 195–200.
- Mukerjee, H. (1988), “Monotone Nonparameteric Regression,” Annals of Statistics, 16, 741–750.
- Nesterov, Y. (2004), Introductory Lectures on Convex Optimization: A Basic Course, Norwell: Kluwer.
- ——— (2005), “Smooth Minimization of Non-Smooth Functions,” Mathematical Programming, 103, 127–152.
- Parikh, N., and Boyd, S. (2014), “Proximal Algorithms,” Foundations and Trends® in Optimization, 1, 127–239.
- Seijo, E., and Sen, B. (2011), “Nonparametric Least Squares Estimation of a Multivariate Convex Regression Function,” Annals of Statistics, 39, 1633–1657.
- Seregin, A., and Wellner, J. A. (2010), “Nonparametric Estimation of Multivariate Convex-Transformed Densities,” Annals of Statistics, 38, 3751–3781, with supplementary material available online.
- Shapiro, A., Dentcheva, D., and Ruszczyński, A. (2009), Lectures on Stochastic Programming: Modeling and Theory, MPS/SIAM Series on Optimization, volume 9, Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM); Mathematical Programming Society (MPS), Philadelphia, PA.
- Van de Geer, S. (2000), Applications of Empirical Process Theory, Cambridge, UK: Cambridge University Press.
- Varian, H. R. (1982), “The Nonparametric Approach to Demand Analysis,” Econometrica, 50, 945–973.
- ——— (1984), “The Nonparametric Approach to Production Analysis,” Econometrica, 52, 579–597.
- Verbeek, M. (2008), A Guide to Modern Econometrics, Chichester, UK: Wiley.
- Wang, Y., and Wang, S. (2013), “Estimating α-Frontier Technical Efficiency With Shape-Restricted Kernel Quantile Regression,” Neurocomputing, 101, 243–251.
- Yatchew, A. (1998), “Nonparametric Regression Techniques in Economics,” Journal of Economic Literature, 36, 669–721.