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An efficient design for model discrimination and parameter estimation in linear models. (English) Zbl 1037.62070

Summary: We consider experimental designs in a regression set-up where the unknown regression function belongs to a known family of nested linear models. The objective of our design is to select the correct model from the family of nested models as well as to estimate efficiently the parameters associated with that model. We show that our proposed design is able to choose the true model with probability tending to one as the number of trials grows to infinity. We also establish that our selected design converges to the optimal design distribution for the true linear model ensuring asymptotic efficiency of least squares estimators of model parameters.

MSC:

62K05 Optimal statistical designs
62L05 Sequential statistical design
62J05 Linear regression; mixed models
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