### Abstract

The Shannon entropy of a random variable X with density function f(x) is defined as H(f) = - ∫ f(x)log f(x) dx. Based on randomly censored observations a nonparametric estimator for H(f) is proposed if H(f) is finite and is nonnegative. This entropy estimator is histogram-based in the sense that it involves a histogram-based density estimator f_{n} constructed from the censored data. We prove the a. s. consistency of this estimator.

Original language | English |
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Pages (from-to) | 441-451 |

Number of pages | 11 |

Journal | Problems of control and information theory |

Volume | 20 |

Issue number | 6 |

Publication status | Published - 1991 |

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### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Problems of control and information theory*,

*20*(6), 441-451.

**Nonparametric entropy estimation based on randomly censored data.** / Carbonez, A.; Györfi, L.; van der Meulen, E. C.

Research output: Contribution to journal › Article

*Problems of control and information theory*, vol. 20, no. 6, pp. 441-451.

}

TY - JOUR

T1 - Nonparametric entropy estimation based on randomly censored data

AU - Carbonez, A.

AU - Györfi, L.

AU - van der Meulen, E. C.

PY - 1991

Y1 - 1991

N2 - The Shannon entropy of a random variable X with density function f(x) is defined as H(f) = - ∫ f(x)log f(x) dx. Based on randomly censored observations a nonparametric estimator for H(f) is proposed if H(f) is finite and is nonnegative. This entropy estimator is histogram-based in the sense that it involves a histogram-based density estimator fn constructed from the censored data. We prove the a. s. consistency of this estimator.

AB - The Shannon entropy of a random variable X with density function f(x) is defined as H(f) = - ∫ f(x)log f(x) dx. Based on randomly censored observations a nonparametric estimator for H(f) is proposed if H(f) is finite and is nonnegative. This entropy estimator is histogram-based in the sense that it involves a histogram-based density estimator fn constructed from the censored data. We prove the a. s. consistency of this estimator.

UR - http://www.scopus.com/inward/record.url?scp=0026289394&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0026289394&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0026289394

VL - 20

SP - 441

EP - 451

JO - Problems of control and information theory

JF - Problems of control and information theory

SN - 0370-2529

IS - 6

ER -