We propose a new unbiased stochastic gradient estimator for a family of stochastic models driven by uniform random numbers as inputs. Dropping the requirement that the tails of the density of the input random variables decay smoothly, the estimator extends the applicability of the generalized likelihood ratio (GLR) method. We demonstrate the new estimator for several general classes of input random variates, including independent inverse transform random variates and dependent input random variables governed by an Archimedean copula. We show how the new estimator works in settings such as density estimation, and we illustrate applications to credit risk derivatives. Numerical experiments substantiate broad applicability and flexibility in dealing with discontinuities in the sample performance.

中文翻译：

---

以均匀随机数作为输入的随机模型的广义似然比方法


我们为一系列由均匀随机数作为输入驱动的随机模型提出了一种新的无偏随机梯度估计器。该估计器放弃了输入随机变量密度的尾部平滑衰减的要求，扩展了广义似然比 （GLR） 方法的适用性。我们演示了几种通用输入随机变量的新估计器，包括独立逆变换随机变量和由阿基米德 copula 控制的因输入随机变量。我们展示了新的估计器在密度估计等环境中是如何工作的，并说明了信用风险衍生品的应用。数值实验证实了在处理样品性能不连续性方面的广泛适用性和灵活性。