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Simulating Gaussian vectors via randomized dimension reduction and PCA

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  • Nabil Kahale

Abstract

We study the problem of estimating E(g(X)), where g is a real-valued function of d variables and X is a d-dimensional Gaussian vector with a given covariance matrix. We present a new unbiased estimator for E(g(X)) that combines the randomized dimension reduction technique with principal components analysis. Under suitable conditions, we prove that our algorithm outperforms the standard Monte Carlo method by a factor of order d.

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  • Nabil Kahale, 2023. "Simulating Gaussian vectors via randomized dimension reduction and PCA," Papers 2304.07377, arXiv.org.
    • Handle: RePEc:arx:papers:2304.07377
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    References listed on IDEAS

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    1. Farshid Jamshidian & Yu Zhu, 1996. "Scenario Simulation: Theory and methodology (*)," Finance and Stochastics, Springer, vol. 1(1), pages 43-67.
    2. Nabil Kahalé, 2020. "Randomized Dimension Reduction for Monte Carlo Simulations," Management Science, INFORMS, vol. 66(3), pages 1421-1439, March.
    3. Yulia Gel & Adrian E. Raftery & Tilmann Gneiting, 2004. "Calibrated Probabilistic Mesoscale Weather Field Forecasting: The Geostatistical Output Perturbation Method," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 575-583, January.
    4. Nabil Kahalé, 2019. "Efficient Simulation of High Dimensional Gaussian Vectors," Mathematics of Operations Research, INFORMS, vol. 44(1), pages 58-73, February.
    5. Paul Glasserman & Jeremy Staum, 2003. "Resource Allocation Among Simulation Time Steps," Operations Research, INFORMS, vol. 51(6), pages 908-921, December.
    6. Daniel Russo & Benjamin Van Roy, 2014. "Learning to Optimize via Posterior Sampling," Mathematics of Operations Research, INFORMS, vol. 39(4), pages 1221-1243, November.
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