Nonparametric link functions with shape constraints in stochastic degradation processes: Application to emerging contaminants

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.