A matrix formalism for the determination of the best estimator in certain simulation-based parameter estimation problems will be presented and discussed. The equations, termed as the Linear Template Fit, combine a linear regression with a least square method and its optimization. The Linear Template Fit employs only predictions that are calculated beforehand and which are provided for a few values of the parameter of interest. Therefore, the Linear Template Fit is particularly suited for parameter estimation with computationally intensive simulations that are otherwise often limited in their usability for statistical inference, or for performance critical applications. Equations for error propagation are discussed, and the analytic form provides comprehensive insights into the parameter estimation problem. Furthermore, the quickly-converging algorithm of the Quadratic Template Fit will be presented, which is suitable for a non-linear dependence on the parameters. As an example application, a determination of the strong coupling constant, $\alpha_s(m_Z)$, from inclusive jet cross section data at the CERN Large Hadron Collider is studied and compared with previously published results.
翻译：将介绍和讨论确定某些模拟参数估计问题中最佳估计符的矩阵形式。方程式称为线性模板Fit,将线性回归与最小平方法及其优化结合起来。线性模板Fit只使用事先计算出来的预测,并且只提供相关参数的几个值。因此,线性模板Fit特别适合参数估算,使用计算密集模拟,这些模拟通常对统计推断或性能关键应用的可用性有限。讨论了错误传播的方程式,分析形式提供了对参数估计问题的全面洞察。此外,将提出快速趋同的夸德式模板Fit算法,该算法适合于对参数的非线性依赖。例如,研究并比较了CERN大哈德伦相交点的包容性喷气截段数据,以确定强烈的组合常数$\alpha_s(m ⁇ )$(m ⁇ )。
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