ABSTRACT
In Chapter 5, we were mainly concerned with the respecification of AIC where the parameter of interest is restricted to be in a closed interval such as A,E[0, 1 ]. We obtained an improved AIC (called PAIC) form in terms of penalty in the presence of such parameter restrictions. A range of simulation experiments has been conducted to see the small sample properties of PAIC, where the probabilities of correct selection from a set of three competing models were calculated and found to vary from one particular design matrix to another. As a result, one could conjecture that these probabilities sometimes can get undesirably uneven (that is, very large for some models while being undesirably small for other models). Consequently, the idea of controlling the probability of correct or incorrect selection seems attractive in the model selection context.
