Recursive computation of inner bounds for the parameters of linear models

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Abstract
Minimum-volume ellipsoidal outer bounds on the parameters of linear regression-type models with bounded model-output error can be computed by an established algorithm. A complementary algorithm to compute maximum-volume ellipsoidal inner bounds is derived. It is little more complicated than the existing outer-bounding algorithm. In conjunction with that algorithm, it allows parameter values to be classified as acceptable, dubious or unacceptable. It is also found to be effective in determining output-error bounds by trial and error during development of parameter-bounding models.