Test of significance in order selection
To select a proper order is a critical step in fitting a model to a data set. It is well known that Mallows' C-p, as well as other asymptotically equivalent order selectors, often selects an excessively targe order. To reduce the chance of overestimating the optimal order using a heavier penalty term has been suggested. In this paper, the issue about setting the penalty term is considered from a perspective similar to hypothesis testing. It is suggested setting the penalty according to the probability of overestimating the true or optimal order. A test procedure based on the order selectors is proposed to assess the significance of the order selected. Some simulation results are presented to illustrate the properties of the order selectors and the test procedure. The application of the procedures to two real examples are also presented.
test of significance order selection linear model