### Abstract

This paper considers the problem of sequential point estimation of the mean of a stable autoregressive process with unknown scale and autoregressive parameters. The construction of a sequential procedure makes use of special stopping rules and some modifications of least-squares estimates. The procedure enables estimating the mean with prescribed mean-square accuracy uniformly in nuisance parameters. The uniform asymptotic normality and the asymptotic minimaxity of the sequential estimate are established. The asymptotic formula for the mean sample size is obtained.

Original language | English |
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Pages (from-to) | 2127-2163 |

Number of pages | 37 |

Journal | Annals of Statistics |

Volume | 25 |

Issue number | 5 |

Publication status | Published - Oct 1997 |

### Keywords

- Autoregression
- Fixed-precision estimators
- Nuisance parameters
- Sequential estimation

### ASJC Scopus subject areas

- Mathematics(all)
- Statistics and Probability

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## Cite this

Konev, V., & Pergamenshchikov, S. (1997). On guaranteed estimation of the mean of an autoregressive process.

*Annals of Statistics*,*25*(5), 2127-2163.