Known Unknowns Versus Unknown Unknowns, and Actual Versus Statistical Significance

Knowing the entire universe of possible outcomes, even if not knowing what particular outcome has occurred, is a situation of known unknowns, and is the domain of risk, whereas not knowing the entire universe of possible outcomes is a situation of unknown unknowns, and is the domain of uncertainty. I provide a measure theoretic generalization of standard probability theory under risk to a theory of generalized probability under uncertainty. I show that the generalized probability measure over its known universe is different from a reconciled probability measure conditioned upon the known universe, but given a random variable and a generalized random variable that are reconciled over a known universe, the expectation of the random variable conditioned upon the known universe equals the expectation of the generalized random variable. I provide a rigorous distinction between public and market information. I replace each variable, except for each indicator or time variable, by the standard cumulative Gaussian probability of its Z-score, therefore, all regression coefficients are systematic, objective, and comparable. I systematically define a full or partial association to be actually significant positive (negative) at level l if the relevant derivative is greater than l (less than -l). I apply these methods to estimate an eight-equation structural system of market efficiency of fixed income securities.MSC Classification Codes: 03; 28; 60; 62; 91