Optimal Estimators of Cross-Partial Derivatives and Surrogates of Functions

Matieyendou Lamboni ()
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Matieyendou Lamboni: Department DFR-ST, University of Guyane, 97346 Cayenne, France

Stats, 2024, vol. 7, issue 3, 1-22

Abstract: Computing cross-partial derivatives using fewer model runs is relevant in modeling, such as stochastic approximation, derivative-based ANOVA, exploring complex models, and active subspaces. This paper introduces surrogates of all the cross-partial derivatives of functions by evaluating such functions at N randomized points and using a set of L constraints. Randomized points rely on independent, central, and symmetric variables. The associated estimators, based on N L model runs, reach the optimal rates of convergence (i.e., O ( N − 1 ) ), and the biases of our approximations do not suffer from the curse of dimensionality for a wide class of functions. Such results are used for (i) computing the main and upper bounds of sensitivity indices, and (ii) deriving emulators of simulators or surrogates of functions thanks to the derivative-based ANOVA. Simulations are presented to show the accuracy of our emulators and estimators of sensitivity indices. The plug-in estimates of indices using the U-statistics of one sample are numerically much stable.

Keywords: derivative-based ANOVA; high-dimensional models; independent input variables; optimal estimators of derivatives; sensitivity analysis (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2024
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