### 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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)
- Statistics and Probability

### Cite this

*Annals of Statistics*,

*25*(5), 2127-2163.

**On guaranteed estimation of the mean of an autoregressive process.** / Konev, V.; Pergamenshchikov, S.

Research output: Contribution to journal › Article

*Annals of Statistics*, vol. 25, no. 5, pp. 2127-2163.

}

TY - JOUR

T1 - On guaranteed estimation of the mean of an autoregressive process

AU - Konev, V.

AU - Pergamenshchikov, S.

PY - 1997/10

Y1 - 1997/10

N2 - 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.

AB - 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.

KW - Autoregression

KW - Fixed-precision estimators

KW - Nuisance parameters

KW - Sequential estimation

UR - http://www.scopus.com/inward/record.url?scp=0031510627&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031510627&partnerID=8YFLogxK

M3 - Article

VL - 25

SP - 2127

EP - 2163

JO - Annals of Statistics

JF - Annals of Statistics

SN - 0090-5364

IS - 5

ER -