## Abstract

Let X _{1}, X _{2},... be an arbitrary random process taking values in a totally bounded subset of a separable metric space. Associated with X _{i} we observe Y _{i} drawn from an unknown conditional distribution F(y|X _{i} = x) with continuous regression function m(x) = E[Y|X = x]. The problem of interest is to estimate Y _{n} based on X _{n} and the data {(X _{i}, Y _{i})} _{i=1} ^{n-1}. We construct appropriate data-dependent nearest neighbor and kernel estimators and show, with a very elementary proof, that these are consistent for every process X _{1,} X _{2}, ....

Original language | English (US) |
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Pages (from-to) | 2785-2788 |

Number of pages | 4 |

Journal | IEEE Transactions on Information Theory |

Volume | 48 |

Issue number | 10 |

DOIs | |

State | Published - Oct 2002 |

## All Science Journal Classification (ASJC) codes

- Information Systems
- Computer Science Applications
- Library and Information Sciences

## Keywords

- Arbitrary random processes
- Consistency
- Data dependent
- Kernel estimate
- Nearest neighbor estimate
- Nonparametric regression

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