We investigate the problem of jointly testing multiple hypotheses and estimating a random parameter of the underlying distribution in a sequential setup. The aim is to jointly infer the true hypothesis and the true parameter while using on average as few samples as possible and keeping the detection and estimation errors below predefined levels. Based on mild assumptions on the underlying model, we propose an asymptotically optimal procedure, i.e., a procedure that becomes optimal when the tolerated detection and estimation error levels tend to zero. The implementation of the resulting asymptotically optimal stopping rule is computationally cheap and, hence, applicable for high-dimensional data. We further propose a projected quasi-Newton method to optimally chose the coefficients that parameterize the instantaneous cost function such that the constraints are fulfilled with equality. The proposed theory is validated by numerical examples.

翻译：我们调查了共同测试多个假设和在顺序设置中估计基本分布随机参数的问题,目的是共同推算真实假设和真实参数,同时平均使用尽可能多的样本,并将探测和估计误差维持在预定水平以下。根据对基本模型的轻度假设,我们建议采用一个非象征性的最佳程序,即当可容忍的检测和估计误差水平趋向于零时,这种程序就变得最佳。因此,无症状的最佳停止规则的实施是计算成本低廉的,因此适用于高维数据。我们进一步提出了预测的准牛顿方法,以最佳选择将即时成本功能参数化的系数,使制约得以平等实现。提议的理论得到数字示例的验证。