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An Empirical, Nonparametric Simulator for Multivariate Random Variables with Differing Marginal Densities and Nonlinear Dependence with Hydroclimatic Applications

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  • Upmanu Lall
  • Naresh Devineni
  • Yasir Kaheil

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.

Suggested Citation

  • Upmanu Lall & Naresh Devineni & Yasir Kaheil, 2016. "An Empirical, Nonparametric Simulator for Multivariate Random Variables with Differing Marginal Densities and Nonlinear Dependence with Hydroclimatic Applications," Risk Analysis, John Wiley & Sons, vol. 36(1), pages 57-73, January.
    • Handle: RePEc:wly:riskan:v:36:y:2016:i:1:p:57-73
    DOI: 10.1111/risa.12432
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    References listed on IDEAS

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    1. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643.
    2. Turvey, Calum G. & Zhao, Jinhua, 1999. "Parametric And Non-Parametric Crop Yield Distributions And Their Effects On All-Risk Crop Insurance Premiums," Working Papers 34129, University of Guelph, Department of Food, Agricultural and Resource Economics.
    3. Kooperberg, Charles & Stone, Charles J., 1991. "A study of logspline density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 12(3), pages 327-347, November.
    4. Mahul, Olivier & Skees, Jerry, 2007. "Managing agricultural risk at the country level : the case of index-based livestock insurance in Mongolia," Policy Research Working Paper Series 4325, The World Bank.
    5. Vitor Ozaki & Barry Goodwin & Ricardo Shirota, 2008. "Parametric and nonparametric statistical modelling of crop yield: implications for pricing crop insurance contracts," Applied Economics, Taylor & Francis Journals, vol. 40(9), pages 1151-1164.
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