Testing for the Important Components of Predictive Variance

ABSTRACT We give a decomposition of the predictive variance based on the law of total variance by making the response variable dependent on a finite dimensional discrete random variable representing our modeling assumptions. Then, we test which terms in this decomposition are small enough to ignore. This allows us to identify which of the discrete random variables, that is, aspects of modeling, are most important to prediction variance. The terms in the decomposition admit interpretations based on conditional means and variances and are analogous to the terms in a Cochran's theorem decomposition of squared error often used in analysis of variance. Thus, the modeling features are treated as factors in completely randomized design.