### Abstract

Consider the regression model Y _{i} = g(t _{i}) + e _{i} for i = 1,...,n. Here -∞ < Y _{i}, e _{i} < ∞, t _{i} ∈ T ⊂ R ^{d}, g ∈ H, and H is a specified class of continuous functions from T to R. Based on a finite series expansion g̃ _{n} of g, an M-estimate ĝ _{n} of g is constructed, and the asymptotic normality of the estimate is investigated. Meanwhile, a test statistic for testing H _{0} : g(·) = g _{0}(·) (a known function) is discussed. We also consider M-estimates for semiparametric regression models and show that they are consistent and asymptotically normal.

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

Pages (from-to) | 1155-1169 |

Number of pages | 15 |

Journal | Statistica Sinica |

Volume | 7 |

Issue number | 4 |

Publication status | Published - 1 Oct 1997 |

### Keywords

- Asymptotic normality
- M-estimation
- Nonparametotic regression model
- Semiparametric regression model
- Spline smoothing technique

## Cite this

Gao, J., & Shi, P. (1997). M-type smoothing splines in nonparametric and semiparametric regression models.

*Statistica Sinica*,*7*(4), 1155-1169.