### Abstract

The article considers univariate density estimation from an individual numerical sequence. It is assumed that (i) the limiting relative frequencies of the numerical sequence are governed by an unknown density, and (ii) there is a known upper bound for the variation of the density an an increasing sequence of intervals. A simple estimation scheme is proposed, and its L_{1} consistency is established when (i) and (ii) apply. In addition it is shown that there is no consistent estimation scheme for the set of individual sequences satisfying only condition (i).

Original language | English |
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Title of host publication | IEEE International Symposium on Information Theory - Proceedings |

Pages | 355 |

Number of pages | 1 |

DOIs | |

Publication status | Published - 1998 |

Event | 1998 IEEE International Symposium on Information Theory, ISIT 1998 - Cambridge, MA, United States Duration: Aug 16 1998 → Aug 21 1998 |

### Other

Other | 1998 IEEE International Symposium on Information Theory, ISIT 1998 |
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Country | United States |

City | Cambridge, MA |

Period | 8/16/98 → 8/21/98 |

### Fingerprint

### ASJC Scopus subject areas

- Applied Mathematics
- Modelling and Simulation
- Theoretical Computer Science
- Information Systems

### Cite this

*IEEE International Symposium on Information Theory - Proceedings*(pp. 355). [708960] https://doi.org/10.1109/ISIT.1998.708960

**Density estimation from an individual numerical sequence.** / Nobel, A. B.; Morvai, G.; Kulkarni, S. R.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*IEEE International Symposium on Information Theory - Proceedings.*, 708960, pp. 355, 1998 IEEE International Symposium on Information Theory, ISIT 1998, Cambridge, MA, United States, 8/16/98. https://doi.org/10.1109/ISIT.1998.708960

}

TY - GEN

T1 - Density estimation from an individual numerical sequence

AU - Nobel, A. B.

AU - Morvai, G.

AU - Kulkarni, S. R.

PY - 1998

Y1 - 1998

N2 - The article considers univariate density estimation from an individual numerical sequence. It is assumed that (i) the limiting relative frequencies of the numerical sequence are governed by an unknown density, and (ii) there is a known upper bound for the variation of the density an an increasing sequence of intervals. A simple estimation scheme is proposed, and its L1 consistency is established when (i) and (ii) apply. In addition it is shown that there is no consistent estimation scheme for the set of individual sequences satisfying only condition (i).

AB - The article considers univariate density estimation from an individual numerical sequence. It is assumed that (i) the limiting relative frequencies of the numerical sequence are governed by an unknown density, and (ii) there is a known upper bound for the variation of the density an an increasing sequence of intervals. A simple estimation scheme is proposed, and its L1 consistency is established when (i) and (ii) apply. In addition it is shown that there is no consistent estimation scheme for the set of individual sequences satisfying only condition (i).

UR - http://www.scopus.com/inward/record.url?scp=84890346426&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84890346426&partnerID=8YFLogxK

U2 - 10.1109/ISIT.1998.708960

DO - 10.1109/ISIT.1998.708960

M3 - Conference contribution

AN - SCOPUS:84890346426

SN - 0780350006

SN - 9780780350007

SP - 355

BT - IEEE International Symposium on Information Theory - Proceedings

ER -