An Empirical,Nonparametric Simulator for Multivariate Random Variables with Differing Marginal Densities and Nonlinear Dependence with Hydroclimatic Applications |
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| Authors: | Upmanu Lall Naresh Devineni Yasir Kaheil |
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| Institution: | 1. Columbia Water Center, Columbia University, New York, NY, USA;2. Department of Earth & Environmental Engineering, Columbia University, New York, NY, USA;3. Department of Civil Engineering, City University of New York (City College), New York, NY, USA;4. NOAA‐Cooperative Remote Sensing Science and Technology Center, City University of New York (City College), New York, NY, USA;5. FM Global, Boston, MA, USA |
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| Abstract: | Multivariate simulations of a set of random variables are often needed for risk analysis. Given a historical data set, the goal is to develop simulations that reproduce the dependence structure in that data set so that the risk of potentially correlated factors can be evaluated. A nonparametric, copula‐based simulation approach is developed and exemplified. It can be applied to multiple variables or to spatial fields with arbitrary dependence structures and marginal densities. The nonparametric simulator uses logspline density estimation in the univariate setting, together with a sampling strategy to reproduce dependence across variables or spatial instances, through a nonparametric numerical approximation of the underlying copula function. The multivariate data vectors are assumed to be independent and identically distributed. A synthetic example is provided to illustrate the method, followed by an application to the risk of livestock losses in Mongolia. |
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| Keywords: | Copula correlated risk logspline multivariate nonparametric simulator spatial fields |
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