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A1615
Title: A minimum-distance estimator for the calibration of simulation models Authors:  Mario Martinoli - University of Insubria (Italy) [presenting]
Raffaello Seri - University of Insubria (Italy)
Abstract: The aim is to propose a new minimum-distance estimator for the calibration of simulation models on real data exploiting a nonparametric smoothing step. Consider a simulation model with parameter space $\Theta$ such that, for any $\theta\in\Theta$, the model can be used to simulate a time series $z^{M}\left(\theta\right)$ of length $M$. We want to calibrate it using an observed time series $y^{N}$ of length $N$. We define $D\left(y^{N},z^{M}\left(\theta\right)\right)$ as the distance between the series. When $N,M\rightarrow\infty$, under suitable assumptions of ergodicity, $D\left(y^{N},z^{M}\left(\theta\right)\right)\rightarrow f\left(\theta\right)$, where $\theta^{\star}=\arg\min_{\theta\in\Theta}f\left(\theta\right)$ is the pseudo-true value of the model. For $\left\{\theta_{i},i=1,\dots,P\right\}$, a finite subset of $\Theta$, one can simulate $z^{M}\left(\theta_{i}\right)$ and the noisy measurements $D\left(y^{N},z^{M}\left(\theta_{i}\right)\right)$ can be used to nonparametrically estimate the function $f$ as $\widehat{f}$, where $\widehat{\theta}=\arg\min_{\theta\in\Theta}\widehat{f}\left(\theta\right)$ is an estimator of $\theta^{\star}$. We investigate the asymptotic properties of this estimator and we provide empirical evidence of its performance.