Smooth Nested Simulation: Bridging Cubic and Square Root Convergence Rates in High Dimensions
References
- (2003) Sobolev Spaces, 2nd ed. (Academic Press, Cambridge, MA).Google Scholar
- (2016) Computing Bayesian means using simulation. ACM Trans. Model. Comput. Simulation 26(2):10.Crossref, Google Scholar
- (2010) Stochastic kriging for simulation metamodeling. Oper. Res. 58(2):371–382.Link, Google Scholar
- (2007) Stochastic Simulation: Algorithm and Analysis (Springer, Berlin).Crossref, Google Scholar
- (2008) Joint inventory and pricing decisions for an assortment. Oper. Res. 56(5):1247–1255.Link, Google Scholar
- (2012) Tutorial: Input uncertainty in output analysis. Laroque C, Himmelspach J, Pasupathy R, Rose O, Uhrmacher AM, eds. Proc. 2012 Winter Simulation Conf. (IEEE, Piscataway, NJ), 67–78.Google Scholar
- (2014) Quantifying input uncertainty via simulation confidence intervals. INFORMS J. Comput. 26(1):74–87.Link, Google Scholar
- (2004) Reproducing Kernel Hilbert Spaces in Probability and Statistics (Springer, Berlin).Crossref, Google Scholar
- (2019) Estimation and prediction using generalized Wendland covariance functions under fixed domain asymptotics. Ann. Statist. 47(2):828–856.Crossref, Google Scholar
- (2018) Optimal rates for regularization of statistical inverse learning problems. Foundations Comput. Math. 18(4):971–1013.Crossref, Google Scholar
- (2019) Where Sobolev interacts with Gagliardo–Nirenberg. J. Functional Anal. 277(8):2839–2864.Crossref, Google Scholar
- (2011) Efficient risk estimation via nested sequential simulation. Management Sci. 57(6):1172–1194.Link, Google Scholar
- (2015) Risk estimation via regression. Oper. Res. 63(5):1077–1097.Link, Google Scholar
- (2007) Optimal rates for the regularized least-squares algorithm. Foundations Comput. Math. 7(3):331–368.Crossref, Google Scholar
- (2001) Input distribution selection for simulation experiments: Accounting for input uncertainty. Oper. Res. 49(5):744–758.Link, Google Scholar
- (2006) Subjective probability and Bayesian methodology. Henderson SG, Nelson BL, eds. Handbooks in Operations Research and Management Science, vol. 13 (Elsevier, Amsterdam), 225–257.Google Scholar
- (2020) Efficient nested simulation for conditional tail expectation of variable annuities. North Amer. Actuarial J. 24(2):187–210.Crossref, Google Scholar
- (2017) Kernel ridge vs. principal component regression: Minimax bounds and the qualification of regularization operators. Electronic J. Statist. 11(1):1022–1047.Crossref, Google Scholar
- (2019) Efficient input uncertainty quantification via green simulation using sample-path likelihood ratios. Mustafee N, Bae K-HG, Lazarova-Molnar S, Rabe M, Szabo C, Haas P, Son Y-J, eds. Proc. 2019 Winter Simulation Conf. (IEEE, Piscataway, NJ), 3693–3704.Google Scholar
- (2021) Optimal nested simulation experiment design via likelihood ratio method. Preprint, submitted July 2, https://arxiv.org/abs/2008.13087.Google Scholar
- (2018) Bayesian optimization. INFORMS TutORials Oper. Res. 255–278.Link, Google Scholar
- (1997) Conditional Monte Carlo: Gradient Estimation and Optimization Applications (Springer, Berlin).Crossref, Google Scholar
- (2009) Conditional Monte Carlo estimation of quantile sensitivities. Management Sci. 55(12):2019–2027.Link, Google Scholar
- (2011) Efficient simulation of value at risk with heavy-tailed risk factors. Oper. Res. 59(6):1395–1406.Link, Google Scholar
- (2003) Monte Carlo Methods in Financial Engineering (Springer, Berlin).Crossref, Google Scholar
- (2000) Variance reduction techniques for estimating value-at-risk. Management Sci. 46(10):1349–1364.Link, Google Scholar
- (2010) Nested simulation in portfolio risk measurement. Management Sci. 56(10):1833–1848.Link, Google Scholar
- (2002) A Distribution-Free Theory of Nonparametric Regression (Springer, Berlin).Crossref, Google Scholar
- (2019) Convergence rates of least squares regression estimators with heavy-tailed errors. Ann. Statist. 47(4):2286–2319.Crossref, Google Scholar
- (2020) Ridge regularization: An essential concept in data science. Technometrics 62(4):426–433.Crossref, Google Scholar
- (2007) The Complete Guide to Option Pricing Formulas, 2nd ed. (McGraw-Hill, New York).Google Scholar
- (2017) Kernel smoothing for nested estimation with application to portfolio risk measurement. Oper. Res. 65(3):657–673.Link, Google Scholar
- (2003) Probabilistic error bounds for simulation quantile estimators. Management Sci. 49(2):230–246.Link, Google Scholar
- (2018) Gaussian processes and kernel methods: A review on connections and equivalences. Preprint, submitted July 6, https://arxiv.org/abs/1807.02582.Google Scholar
- (2010) Two-level simulation of expected shortfall: Confidence intervals, efficient simulation procedures, and high-performance computing. PhD thesis, Northwestern University, Evanston, IL.Google Scholar
- (2010) A confidence interval procedure for expected shortfall risk measurement via two-level simulation. Oper. Res. 58(5):1481–1490.Link, Google Scholar
- (2003) Computing the distribution function of a conditional expectation via Monte Carlo: Discrete conditioning spaces. ACM Trans. Model. Comput. Simulation 13(3):238–258.Crossref, Google Scholar
- (2007) Simulation of coherent risk measures based on generalized scenarios. Management Sci. 53(11):1756–1769.Link, Google Scholar
- (2020) Fast and efficient nested simulation for large variable annuity portfolios: A surrogate modeling approach. Insurance Math. Econom. 91:85–103.Crossref, Google Scholar
- (2010) Stochastic kriging for efficient nested simulation of expected shortfall. J. Risk 12(3):3–27.Crossref, Google Scholar
- (2020) Online quantification of input model uncertainty by two-layer importance sampling. Preprint, submitted February 12, https://arxiv.org/abs/1912.11172.Google Scholar
- (2022) Random features for kernel approximation: A survey on algorithms, theory, and beyond. IEEE Trans. Pattern Anal. Machine Intelligence 44(10):7128–7148.Crossref, Google Scholar
- (2020) Faster kriging: Facing high-dimensional simulators. Oper. Res. 68(1):233–249.Link, Google Scholar
- (1990) The tight constant in the Dvoretzky–Kiefer–Wolfowitz inequality. Ann. Probab. 18(3):1269–1283.Crossref, Google Scholar
- (2013) The multi-armed bandit problem with covariates. Ann. Statist. 41(2):693–721.Crossref, Google Scholar
- (2006) Gaussian Processes for Machine Learning (MIT Press, Cambridge, MA).Google Scholar
- (2002) Conditional value-at-risk for general loss distributions. J. Banking Finance 26(7):1443–1471.Crossref, Google Scholar
- (2019) Generalized integrated Brownian fields for simulation metamodeling. Oper. Res. 67(3):874–891.Link, Google Scholar
- (2002) Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond (MIT Press, Cambridge, MA).Google Scholar
- (2016) Taking the human out of the loop: A review of Bayesian optimization. Proc. IEEE 104(1):148–175.Crossref, Google Scholar
- (2009) Optimal rates for regularized least squares regression. Dasgupta S, Klivans A, eds. Proc. 22nd Annual Conf. Learn. Theory, 79–93.Google Scholar
- (2011) Efficient nested simulation for estimating the variance of a conditional expectation. Oper. Res. 59(4):998–1007.Link, Google Scholar
- (2004) Optimal aggregation of classifiers in statistical learning. Ann. Statist. 32(1):135–166.Crossref, Google Scholar
- (2020) On the improved rates of convergence for Matérn-type kernel ridge regression with application to calibration of computer models. SIAM/ASA J. Uncertainty Quantification 8(4):1522–1547.Crossref, Google Scholar
- (2021) Bayesian optimization is superior to random search for machine learning hyperparameter tuning: Analysis of the black-box optimization challenge 2020. Escalante HJ, Hofmann K, eds. Proc. NeurIPS 2020 Competition and Demonstration Track (PMLR, New York), 3–26.Google Scholar
- (2000) Empirical Processes in M-Estimation (Cambridge University Press, Cambridge, UK).Google Scholar
- (2019) High-Dimensional Statistics: A Non-Asymptotic Viewpoint (Cambridge University Press, Cambridge, UK).Crossref, Google Scholar
- (2021) A nonparametric Bayesian approach for simulation optimization with input uncertainty. Preprint, submitted January 27, https://arxiv.org/abs/2008.02154v2.Google Scholar
- (2018) A Bayesian risk approach to data-driven stochastic optimization: Formulations and asymptotics. SIAM J. Optim. 28(2):1588–1612.Crossref, Google Scholar
- (2014) A Bayesian framework for quantifying uncertainty in stochastic simulation. Oper. Res. 62(6):1439–1452.Link, Google Scholar
- (2015) Divide and conquer kernel ridge regression: A distributed algorithm with minimax optimal rates. J. Machine Learn. Res. 16(102):3299–3340.Google Scholar
- (2022a) Technical note—Bootstrap-based budget allocation for nested simulation. Oper. Res. 70(2):1128–1142.Link, Google Scholar
- (2022b) Sample recycling for nested simulation with application in portfolio risk measurement. Preprint, submitted March 29, https://arxiv.org/abs/2203.15929.Google Scholar
- (2018) Online quantification of input uncertainty for parametric models. Rabe M, Juan AA, Mustafee N, Skoogh A, Jain S, Johansson B, eds. Proc. 2018 Winter Simulation Conf. (IEEE, Piscataway, NJ), 1587–1598.Google Scholar
- (2020) Risk quantification in stochastic simulation under input uncertainty. ACM Trans. Model. Comput. Simulation 30(1):1.Crossref, Google Scholar

