### Abstract

The nonparametric regression problem has the objective of estimating conditional expectation. Consider the model {Mathematical expression}, where the random variable Z has mean zero and is independent of X. The regression function R(x) is the conditional expectation of Y given X = x. For an estimator of the form {Mathematical expression}, we obtain the rate of strong uniform convergence {Mathematical expression}. Here X is a d-dimensional variable and C is a suitable subset of R^{d}.

Original language | English |
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Pages (from-to) | 177-187 |

Number of pages | 11 |

Journal | Periodica Mathematica Hungarica |

Volume | 14 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jun 1983 |

Externally published | Yes |

### Keywords

- AMS (MOS) subject classifications (1970): Primary 62G05, Secondary 60F15
- Nonparametric regression
- strong convergence

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Cheng, K. F. (1983). Strong convergence in nonparametric estimation of regression functions.

*Periodica Mathematica Hungarica*,*14*(2), 177-187. https://doi.org/10.1007/BF01855429