Abstract Effective oxidation-based elimination of emerging contaminants (ECs) requires a good understanding of the effects of treatment conditions, such as the kinds and dosages of reagents, on the EC degradation rate. Due to limited knowledge on the complex reaction mechanism and the multiple covariates to represent the treatment conditions, it is generally hard to parametrically quantify the relation between these covariates and the degradation rate. On the other hand, qualitative analysis based on chemical mechanisms often provides shape information of the covariate–rate relation, such as monotonicity and local concavity in each coordinate. Based on the chemical kinetics, we use stationary stochastic processes for parametric modeling of log-transformed EC degradation under each combination of the treatment conditions. The tensor-product Bernstein bases are then used to approximate the covariate–rate relation. The shape information is naturally translated to constraints on the coefficients of the bases functions. Likelihood-based inference procedures are developed for both point and interval estimation in the proposed models. Simulation results show that the use of shape information significantly improves the accuracy of estimates. The proposed method is successfully applied to EC degradation data collected from real experiments.

中文翻译：

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随机降解过程中具有形状约束的非参数链接函数：对新兴污染物的应用

摘要 新出现污染物 (ECs) 的有效氧化消除需要很好地了解处理条件的影响，例如试剂的种类和剂量，对 EC 降解率的影响。由于对复杂反应机制和表示处理条件的多个协变量的了解有限，通常很难参数化量化这些协变量与降解率之间的关系。另一方面，基于化学机制的定性分析通常提供协变量-速率关系的形状信息，例如每个坐标的单调性和局部凹度。基于化学动力学，我们使用平稳随机过程对每种处理条件组合下对数转换的 EC 降解进行参数建模。然后使用张量积 Bernstein 基来近似协变量-速率关系。形状信息自然地转换为对基函数系数的约束。为所提出的模型中的点估计和区间估计开发了基于似然的推理程序。仿真结果表明，形状信息的使用显着提高了估计的准确性。所提出的方法成功地应用于从实际实验中收集的 EC 降解数据。仿真结果表明，形状信息的使用显着提高了估计的准确性。所提出的方法成功地应用于从实际实验中收集的 EC 降解数据。仿真结果表明，形状信息的使用显着提高了估计的准确性。所提出的方法成功地应用于从实际实验中收集的 EC 降解数据。