A bootstrap‐based method for optimal design of experiments. (10th August 2016)

• Record Type: Journal Article
• Authors: Paquet‐Durand, O.; Zettel, V.; Hitzmann, B.
• Is Part Of: Journal of chemometrics. Volume 30:Number 10(2016)
• Page Start: 567
• Page End: 574
• Publication Date: 2016-08-10
• Subjects: bootstrapping -- Cramér‐Rao lower bound -- optimal design of experiments -- Peleg model -- water absorption; Chemistry -- Mathematics -- Periodicals; Chemistry -- Statistical methods -- Periodicals; 542.85
• DOI: 10.1002/cem.2820
• Languages: English
• ISSNs: 0886-9383

Abstract

Abstract : Bootstrapping can be used for the estimation of parameter variances, and it is straightforward to be implemented but computationally demanding compared with other methods for parameter error estimation. It is not bound to any restrictions such as the distribution of measurement errors. And because of the possible asymmetry of the probability densities of the parameters, the parameter estimation errors acquired by bootstrapping are likely to be more accurate. In this work the feasibility of a bootstrap‐based method for optimal experimental design was evaluated for the Peleg model. The optimal design was performed, based on the Cramér‐Rao lower bound as a benchmark. Afterwards, the optimal design was calculated based on the bootstrap method. It is demonstrated that a bootstrap‐based optimal design of experiments will give comparable results with the Cramér‐Rao lower bound optimal designs, however with slightly different measurement points in time. If the parameter errors obtained from both optimal experimental designs are compared, they deviate for the 2 methods on average by 1.5%. Bootstrapping can be used for problems, which cannot be solved using Cramér‐Rao lower bound because of necessary but invalid assumptions. However, the benefits of the bootstrap method come at the cost of a significant increase in computational effort. Under similar conditions, the computation time for a bootstrap‐based optimal design was 25 minutes compared with 5 seconds when using the Cramér‐Rao lower bound method. As computers get faster and faster over time, the increase in computational demand will probably become less relevant in the future. Abstract : In this contribution, an optimal design of experiments for the determination of the parameters of the Peleg model has been performed. For the parameter error estimation, a bootstrap‐based approach has been used and has been compared to the normal Cramér‐Rao lower bound method. Although bootstrapping is computationally more demanding, it has no requirements on the distributions of the measurements or the parameter values. Therefore, it is more flexible and has the potential to be more accurate.