Layman’s abstract for Stat article on a constrained minimum method for model selection

Each week, we publish layman’s abstracts of new articles from our prestigious portfolio of journals in statistics. The aim is to highlight the latest research to a broader audience in an accessible format.
The article featured today is from Stat, with the full article now available to read here.
Tsao, M. (2021). A constrained minimum method for model selectionStat101), e387.
This paper introduces a new model selection method for Gaussian linear models based on the likelihood ratio test for the parameter vector of a linear model. The paper shows that when the sample size is large, with a properly chosen significance level there is a high probability that the smallest model not rejected by the test is the true model containing only and all active variables. The paper thus advocates selecting the smallest model not rejected by the test and calls this the constrained minimum criterion (CMC) for model selection. A numerical comparison with several commonly used model selection criteria, including the AIC and BIC, shows the CMC has very good accuracy. The CMC can control the balance between the false active rate and false inactive rate of the selected model through the significance level of the likelihood ratio test. It can also be extended to handle model selection problems for other types of models such as nonlinear models and generalized linear models.
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