2016/07/05 by Kalyani Nagaraj, Nagaraj, Kalyani, Jie Xu +5
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #Computation (stat.CO) #FOS: Computer and information sciences #Financial Risk and Volatility Modeling #Insurance, Mortality, Demography, Risk Management #Machine Learning (stat.ML) #Probability and Risk Models
paper · pdf · doi:10.48550/arxiv.1607.01375
openalex publication_date 2016/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the question of efficient estimation in the tails of Gaussian copulas. Our special focus is estimating expectations over multi-dimensional constrained sets that have a small implied measure under the Gaussian copula. We propose three estimators, all of which rely on a simple idea: identify certain dominating point(s) of the feasible set, and appropriately shift and scale an exponential distribution for subsequent use within an importance sampling measure. As we show, the efficiency of such estimators depends crucially on the local structure of the feasible set around the dominating points. The first of our proposed estimators \estOpt is the "full-information" estimator that actively exploits such local structure to achieve bounded relative error in Gaussian settings. The second and third estimators \estExp, \estLap are "partial-information" estimators, for use when complete information about the constraint set is not available, they do not exhibit bounded relative error but are shown to achieve polynomial efficiency. We provide sharp asymptotics for all three estimators. For the NORTA setting where no ready information about the dominating points or the feasible set structure is assumed, we construct a multinomial mixture of the partial-information estimator \estLap resulting in a fourth estimator \estNt with polynomial efficiency, and implementable through the ecoNORTA algorithm. Numerical results on various example problems are remarkable, and consistent with theory.