Comparison of Two Robust Alternatives to the Box–Draper Determinant Criterion in Multiresponse Kinetic Parameter Estimation

Abstract

Generalized least-squares and maximum likelihood approaches for parameter estimation in multivariate response models have been prevalent in the chemical kinetics literature to date. In contrast, robust alternatives have received considerably less attention. These methods safeguard against possible deviations from the assumptions, such as the presence of outliers or non-normality of the random errors. We compare, through Monte Carlo simulation, the performance of the classical Box–Draper determinant criterion (ML) to those of two robust estimators: the multivariate Huber’s M-estimator and the multivariate least-trimmed squares estimator (MLTS). Although the results are not entirely conclusive, overall, we find no compelling evidence for preferring any one of the two robust methods over the conventional ML estimates. At the same time, it was unexpected to find that ML is still reasonable under mild outlier contamination and mild deviations from normality. This notwithstanding, one loses nothing by comparing ML together with MLTS to cross-check each other as a safety measure.

Discrete element method modeling of biomass fast pyrolysis granular flows

“…Central to this realization in the model development is the formation of optimization objective functions from multiple responses. Although least squares or weighted least squares functions are often formulated as the optimization targets in previous model developments [164,165,166,167], they have been reported to have limitations when dealing with multi-response data [169,171]. In order to avoid this problem, multiple objectives are optimized simultaneously instead of combining them into one single objective.…”