Preprint #96-18
That Probabilities Rather than Likelihoods Should be
Maximized
by
C. Philip Cox
Abstract
Parameters of models posited for discrete variates are estimated by
maximizing the joint probabilities of occurrence for the observed
discrete values. The corresponding procedure for continuous
variates is to maximize likelihood, a quantity which approximates the
joint probability of occurrence when multiplied by appropriate
differentials. Discussion of an example in the context of `compound'
linear regression - wherein `measurement' variability attends both
the x and y variables - shows that maximizing likelihood can be
misleading and that the deficiency can be avoided by maximizing the
approximate joint probability of occurrence.
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make the request directly to the author, Iowa State
University,
Department of Statistics, Snedecor Hall, Ames, IA 50011-1210.