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The information criterion (IC) rule and the generalized likelihood ratio test (GLRT) have been usually considered to be two rather different approaches to model order selection. However, we show here that a natural implementation of the GLRT is, in fact, equivalent to the IC rule. A consequence of this equivalence is that a specific IC rule, such as Akaike IC or Bayesian IC, can be viewed as a more direct way of implementing a GLRT with a specific threshold. Another consequence of the equivalence, which is emphasized herein, is a possibly original way of exploiting the information provided by the local behavior of an IC for selecting the structure of sparse models (the parameter vectors of which comprise "many" elements equal to zero).