The Choice of an Admissible Set of k Non-nested Models

Suppose we have a random sample of size n of a population with true density h(.). In general, h(.) is unknown and we use the model f as an approximation of this density function. We do inference based on f. Clearly, f must be close to the true density h, to reach a valid inference about the population. The suggestion of an absolute model based on a few obsevations, as an approximation or estimation of the true density, h, results a great risk in the model selection. For this reason, we choose k non-nested models and investigate the model which is closer to the true density. In this paper, we investigate this main question in the model selection that how is it possible to gain a collection of appropriate models for the estimation of the true density function h, based on Kullback-Leibler risk.