The Annals of Statistics

Sequential Estimation of the Mean of a First-Order Stationary Autoregressive Process

T. N. Sriram

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Abstract

This paper considers the problem of sequential point and fixed-width confidence interval estimation of the location parameter when the errors form an autoregressive process with unknown scale and autoregressive parameters. The sequential point estimator considered here is based on sample mean and is shown to be asymptotically risk efficient as the cost per observation tends to zero. The sequential interval estimator is shown to be asymptotically consistent and the corresponding stopping rule is shown to be asymptotically efficient as the width of the interval tends to zero.

Article information

Source
Ann. Statist., Volume 15, Number 3 (1987), 1079-1090.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176350494

Digital Object Identifier
doi:10.1214/aos/1176350494

Mathematical Reviews number (MathSciNet)
MR902247

Zentralblatt MATH identifier
0627.62084

JSTOR
links.jstor.org

Subjects
Primary: 62L12: Sequential estimation
Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]

Keywords
Asymptotic risk efficiency asymptotic consistency asymptotic efficiency Burkholder inequality Marcinkiewicz-Zygmund inequality reverse martingale

Citation

Sriram, T. N. Sequential Estimation of the Mean of a First-Order Stationary Autoregressive Process. Ann. Statist. 15 (1987), no. 3, 1079--1090. doi:10.1214/aos/1176350494. https://projecteuclid.org/euclid.aos/1176350494


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