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A Monte Carlo based analysis of optimal design criteria. (English) Zbl 1279.93056

Summary: Optimal design methods (designed to choose optimal sampling distributions through minimization of a specific cost function related to the resulting error in parameter estimates) for inverse or parameter estimation problems are considered. We compare a recent design criteria, SE-optimal design (standard error optimal design) with the more traditional D-optimal and E-optimal designs. The optimal sampling distributions from each design are used to compute and compare standard errors; here the standard errors for parameters are computed using the optimal mesh along with Monte Carlo simulations as compared to asymptotic theory based standard errors. We illustrate ideas with two examples: the Verhulst-Pearl logistic population model and the standard harmonic oscillator model.

MSC:

93B51 Design techniques (robust design, computer-aided design, etc.)
62B10 Statistical aspects of information-theoretic topics
62B15 Theory of statistical experiments
62G08 Nonparametric regression and quantile regression
62H12 Estimation in multivariate analysis
90C31 Sensitivity, stability, parametric optimization
65C05 Monte Carlo methods
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