Motivated by the goal of improving the efficiency of small sample design, we propose a novel Bayesian stochastic approximation method to estimate the root of a regression function. The method features adaptive local modelling and nonrecursive iteration. Strong consistency of the Bayes estimator is obtained. Simulation studies show that our method is superior in finite-sample performance to Robbins--Monro type procedures. Extensions to searching for extrema and a version of generalized multivariate quantile are presented.

中文翻译：

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一种贝叶斯随机逼近方法

出于提高小样本设计效率的目标，我们提出了一种新颖的贝叶斯随机近似方法来估计回归函数的根。该方法具有自适应局部建模和非递归迭代的特点。获得了贝叶斯估计量的强一致性。仿真研究表明，我们的方法在有限样本性能方面优于 Robbins--Monro 类型程序。提供了搜索极值的扩展和广义多元分位数的一个版本。