### Abstract

Cubic B-splines are used to estimate the nonparametric component of a semiparametric generalized linear model. A penalized log-likelihood ratio test statistic is constructed for the null hypothesis of the linearity of the nonparametric function. When the number of knots is fixed, its limiting null distribution is the distribution of a linear combination of independent chi-squared random variables, each with one df. The smoothing parameter is determined by giving a specified value for its asymptotically expected value under the null hypothesis. A simulation study is conducted to evaluate its power performance; a real-life dataset is used to illustrate its practical use.

Original language | English (US) |
---|---|

Pages (from-to) | 4240-4250 |

Number of pages | 11 |

Journal | Communications in Statistics - Theory and Methods |

Volume | 41 |

Issue number | 23 |

DOIs | |

State | Published - Dec 1 2012 |

### Fingerprint

### Keywords

- B-spline
- Generalized linear model
- Generalized partially linear model
- Penalized log-likelihood ratio test
- Semiparametric generalized linear model

### ASJC Scopus subject areas

- Statistics and Probability

### Cite this

**Lack-of-fit tests for generalized linear models via splines.** / Li, Chin-Shang.

Research output: Contribution to journal › Article

*Communications in Statistics - Theory and Methods*, vol. 41, no. 23, pp. 4240-4250. https://doi.org/10.1080/03610926.2011.568157

}

TY - JOUR

T1 - Lack-of-fit tests for generalized linear models via splines

AU - Li, Chin-Shang

PY - 2012/12/1

Y1 - 2012/12/1

N2 - Cubic B-splines are used to estimate the nonparametric component of a semiparametric generalized linear model. A penalized log-likelihood ratio test statistic is constructed for the null hypothesis of the linearity of the nonparametric function. When the number of knots is fixed, its limiting null distribution is the distribution of a linear combination of independent chi-squared random variables, each with one df. The smoothing parameter is determined by giving a specified value for its asymptotically expected value under the null hypothesis. A simulation study is conducted to evaluate its power performance; a real-life dataset is used to illustrate its practical use.

AB - Cubic B-splines are used to estimate the nonparametric component of a semiparametric generalized linear model. A penalized log-likelihood ratio test statistic is constructed for the null hypothesis of the linearity of the nonparametric function. When the number of knots is fixed, its limiting null distribution is the distribution of a linear combination of independent chi-squared random variables, each with one df. The smoothing parameter is determined by giving a specified value for its asymptotically expected value under the null hypothesis. A simulation study is conducted to evaluate its power performance; a real-life dataset is used to illustrate its practical use.

KW - B-spline

KW - Generalized linear model

KW - Generalized partially linear model

KW - Penalized log-likelihood ratio test

KW - Semiparametric generalized linear model

UR - http://www.scopus.com/inward/record.url?scp=84867756259&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84867756259&partnerID=8YFLogxK

U2 - 10.1080/03610926.2011.568157

DO - 10.1080/03610926.2011.568157

M3 - Article

AN - SCOPUS:84867756259

VL - 41

SP - 4240

EP - 4250

JO - Communications in Statistics - Theory and Methods

JF - Communications in Statistics - Theory and Methods

SN - 0361-0926

IS - 23

ER -