## Abstract

Consider the regression model Y_{i}= g(x_{i}) + e_{i}, i = 1,…, n, where g is an unknown function defined on [0, 1], 0 = x_{0} < x_{1} < … < x_{n}≤ 1 are chosen so that max_{1≤i≤n}(x_{i}‐x_{i‐ 1}) = 0(n^{‐1}), and where {e_{i}} are i.i.d. with Ee_{1}= 0 and Var e_{1} ‐ s̀^{2}. In a previous paper, Cheng & Lin (1979) study three estimators of g, namely, g_{1n} of Cheng & Lin (1979), g_{2n} of Clark (1977), and g_{3n} of Priestley & Chao (1972). Consistency results are established and rates of strong uniform convergence are obtained. In the current investigation the limiting distribution of &_{in}, i = 1, 2, 3, and that of the isotonic estimator g**_{n} are considered.

Original language | English |
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Pages (from-to) | 186-195 |

Number of pages | 10 |

Journal | Australian Journal of Statistics |

Volume | 23 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1981 |

Externally published | Yes |

## Keywords

- Asymptotic normality
- Berry‐Esséen bound
- Isotonic
- Kernel function
- Liapunov's theorem
- Lipschitz
- phrases

## ASJC Scopus subject areas

- Statistics and Probability