### Abstract

The product limit estimator {Mathematical expression} of an unknown distribution F is represented as a U-statistic plus an error of the order o(1/n). Using this, the maximum likelihood estimator of the specific risk rate in the time interval [0, M], is shown to admit a two term Edgeworth expansion. This risk rate for a specific cause of death is defined as the ratio of the probability of death, due to that particular cause, in the time interval [0, M], to the mean life time of an individual up to that time point M. Similar expansions for the bootstrapped statistics are used to show that the bootstrap distribution, of the studentized estimator of the risk rate, approximates the sampling distribution better than the corresponding normal distribution.

Original language | English (US) |
---|---|

Pages (from-to) | 275-290 |

Number of pages | 16 |

Journal | Probability Theory and Related Fields |

Volume | 90 |

Issue number | 2 |

DOIs | |

State | Published - Jun 1 1991 |

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### All Science Journal Classification (ASJC) codes

- Analysis
- Statistics and Probability
- Statistics, Probability and Uncertainty

### Cite this

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*Probability Theory and Related Fields*, vol. 90, no. 2, pp. 275-290. https://doi.org/10.1007/BF01192165

**Asymptotic theory for estimators under random censorship.** / Babu, G. Jogesh.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Asymptotic theory for estimators under random censorship

AU - Babu, G. Jogesh

PY - 1991/6/1

Y1 - 1991/6/1

N2 - The product limit estimator {Mathematical expression} of an unknown distribution F is represented as a U-statistic plus an error of the order o(1/n). Using this, the maximum likelihood estimator of the specific risk rate in the time interval [0, M], is shown to admit a two term Edgeworth expansion. This risk rate for a specific cause of death is defined as the ratio of the probability of death, due to that particular cause, in the time interval [0, M], to the mean life time of an individual up to that time point M. Similar expansions for the bootstrapped statistics are used to show that the bootstrap distribution, of the studentized estimator of the risk rate, approximates the sampling distribution better than the corresponding normal distribution.

AB - The product limit estimator {Mathematical expression} of an unknown distribution F is represented as a U-statistic plus an error of the order o(1/n). Using this, the maximum likelihood estimator of the specific risk rate in the time interval [0, M], is shown to admit a two term Edgeworth expansion. This risk rate for a specific cause of death is defined as the ratio of the probability of death, due to that particular cause, in the time interval [0, M], to the mean life time of an individual up to that time point M. Similar expansions for the bootstrapped statistics are used to show that the bootstrap distribution, of the studentized estimator of the risk rate, approximates the sampling distribution better than the corresponding normal distribution.

UR - http://www.scopus.com/inward/record.url?scp=0040510130&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0040510130&partnerID=8YFLogxK

U2 - 10.1007/BF01192165

DO - 10.1007/BF01192165

M3 - Article

AN - SCOPUS:0040510130

VL - 90

SP - 275

EP - 290

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

SN - 0178-8051

IS - 2

ER -