### Abstract

We consider the model (subset) selection problem for linear regression. Although hypothesis testing and model selection are two different approaches, there are similarities between them. In this article we combine these two approaches together and propose a particular choice of the penalty parameter in the generalized information criterion (GIC), which leads to a model selection procedure that inherits good properties from both approaches, i.e., its overfitting and underfitting probabilities converge to 0 as the sample size n→∞ and, when n is fixed, its overfitting probability is controlled to be approximately under a pre-assigned level of significance.

Original language | English |
---|---|

Pages (from-to) | 215-231 |

Number of pages | 17 |

Journal | Journal of Statistical Planning and Inference |

Volume | 88 |

Issue number | 2 |

State | Published - Aug 1 2000 |

Externally published | Yes |

### Fingerprint

### Keywords

- 62J05
- Hypothesis testing
- Information criteria* Linear regression
- Prediction error

### ASJC Scopus subject areas

- Statistics, Probability and Uncertainty
- Applied Mathematics
- Statistics and Probability

### Cite this

*Journal of Statistical Planning and Inference*,

*88*(2), 215-231.

**The GIC for model selection : A hypothesis testing approach.** / Shao, Jun; Rao, Jonnagadda S.

Research output: Contribution to journal › Article

*Journal of Statistical Planning and Inference*, vol. 88, no. 2, pp. 215-231.

}

TY - JOUR

T1 - The GIC for model selection

T2 - A hypothesis testing approach

AU - Shao, Jun

AU - Rao, Jonnagadda S

PY - 2000/8/1

Y1 - 2000/8/1

N2 - We consider the model (subset) selection problem for linear regression. Although hypothesis testing and model selection are two different approaches, there are similarities between them. In this article we combine these two approaches together and propose a particular choice of the penalty parameter in the generalized information criterion (GIC), which leads to a model selection procedure that inherits good properties from both approaches, i.e., its overfitting and underfitting probabilities converge to 0 as the sample size n→∞ and, when n is fixed, its overfitting probability is controlled to be approximately under a pre-assigned level of significance.

AB - We consider the model (subset) selection problem for linear regression. Although hypothesis testing and model selection are two different approaches, there are similarities between them. In this article we combine these two approaches together and propose a particular choice of the penalty parameter in the generalized information criterion (GIC), which leads to a model selection procedure that inherits good properties from both approaches, i.e., its overfitting and underfitting probabilities converge to 0 as the sample size n→∞ and, when n is fixed, its overfitting probability is controlled to be approximately under a pre-assigned level of significance.

KW - 62J05

KW - Hypothesis testing

KW - Information criteria Linear regression

KW - Prediction error

UR - http://www.scopus.com/inward/record.url?scp=0042708473&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0042708473&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0042708473

VL - 88

SP - 215

EP - 231

JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

SN - 0378-3758

IS - 2

ER -