### Abstract

A spline-based test statistic for a constant mean function is proposed based on the penalized residual sum-of-squares difference between the null model and a B-spline model in which the regression function is approximated with P-splines approach. When the number of knots is fixed, the limiting null distribution of the test statistic is shown to be the distribution of a linear combination of independent chi-squared random variables, each with one degree of freedom. A smoothing parameter is selected by setting a specified value equal to the expected value of the test statistic under the null hypothesis. Simulation experiments are conducted to study the proposed spline-based test statistic's finite-sample properties.

Original language | English (US) |
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Pages (from-to) | 343-357 |

Number of pages | 15 |

Journal | Computational Statistics |

Volume | 27 |

Issue number | 2 |

DOIs | |

State | Published - Jun 2012 |

### Fingerprint

### Keywords

- B-spliness
- P-splines
- Penalized least-squares
- Spline-based test

### ASJC Scopus subject areas

- Statistics and Probability
- Computational Mathematics
- Statistics, Probability and Uncertainty

### Cite this

*Computational Statistics*,

*27*(2), 343-357. https://doi.org/10.1007/s00180-011-0260-6

**Testing for no effect via splines.** / Li, Chin-Shang.

Research output: Contribution to journal › Article

*Computational Statistics*, vol. 27, no. 2, pp. 343-357. https://doi.org/10.1007/s00180-011-0260-6

}

TY - JOUR

T1 - Testing for no effect via splines

AU - Li, Chin-Shang

PY - 2012/6

Y1 - 2012/6

N2 - A spline-based test statistic for a constant mean function is proposed based on the penalized residual sum-of-squares difference between the null model and a B-spline model in which the regression function is approximated with P-splines approach. When the number of knots is fixed, the limiting null distribution of the test statistic is shown to be the distribution of a linear combination of independent chi-squared random variables, each with one degree of freedom. A smoothing parameter is selected by setting a specified value equal to the expected value of the test statistic under the null hypothesis. Simulation experiments are conducted to study the proposed spline-based test statistic's finite-sample properties.

AB - A spline-based test statistic for a constant mean function is proposed based on the penalized residual sum-of-squares difference between the null model and a B-spline model in which the regression function is approximated with P-splines approach. When the number of knots is fixed, the limiting null distribution of the test statistic is shown to be the distribution of a linear combination of independent chi-squared random variables, each with one degree of freedom. A smoothing parameter is selected by setting a specified value equal to the expected value of the test statistic under the null hypothesis. Simulation experiments are conducted to study the proposed spline-based test statistic's finite-sample properties.

KW - B-spliness

KW - P-splines

KW - Penalized least-squares

KW - Spline-based test

UR - http://www.scopus.com/inward/record.url?scp=84860360538&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84860360538&partnerID=8YFLogxK

U2 - 10.1007/s00180-011-0260-6

DO - 10.1007/s00180-011-0260-6

M3 - Article

VL - 27

SP - 343

EP - 357

JO - Computational Statistics

JF - Computational Statistics

SN - 0943-4062

IS - 2

ER -