Speaker
Description
Identifiability of polynomial models is a key requirement for multiple
regression. We consider an analogue of the so-called statistical fan, the set of
all maximal identifiable hierarchical models, for cases of noisy design of experiments or measured covariate vectors with a given tolerance vector. This
gives rise to the definition of the numerical statistical fan. It includes all
maximal hierarchical models that avoid approximate linear dependence of the
design vectors. We develop an algorithm to compute the numerical statistical
fan using recent results on the computation of all border bases of a design
ideal from the field of algebra.
In the low-dimensional case and for sufficiently small data sets the numerical statistical fan is effectively computable and much smaller than the respective statistical fan. The gained
enhanced knowledge of the space of all stable identifiable hierarchical models
enables improved model selection procedures. We combine the recursive computation of the numerical statistical fan with model selection procedures for linear models and GLMs, and we provide implementations in R.
| Keywords | identi fiable regression models, hierarchical models, noisy experimental design |
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