Work by Robert Kalaba on multicriteria estimation

摘要

For many processes of interest, particularly in the socio-economic and biological sciences, the underlying relationships are not yet well understood. Consequently, aside from identities, model equations tend to be rough approximations at best. It therefore can be both inappropriate and fundamentally misleading to adopt, as a routine practice, the standard statistical inference assumption that model discrepancy terms (i.e., model specification errors) are commensurable random quantities governed by meaningful probability relations. For the past twelve years, Robert Kalaba has explored the consequences for statistical inference which result from these common-sense observations. One consequence, in particular, is that multicriteria methods take on a new and critical importance. This paper explains, by example, his multicriteria re-formulation of the basic estimation problem, the reconciliation of imperfect theory with observations.