### 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 | |

Publication status | Published - Jun 2012 |

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### 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