The Annals of Statistics

Estimation in the General Linear Model when the Accuracy is Specified Before Data Collection

Mark Finster

Full-text: Open access

Abstract

An estimator $\hat{\beta}$ of $\beta$ is accurate with accuracy $A$ and confidence $\gamma, 0 < \gamma < 1,$ if $P(\hat{\beta} - \beta \in A) \geq \gamma$ for all $\beta.$ Given a sequence $Y_1, Y_2, \cdots$ of independent vector-valued homoscedastic normally-distributed random variables generated via the general linear model $Y_i = X_i\beta + \varepsilon,$ the $k$-dimensional parameter $\beta$ is accurately estimated using a sequential version of the maximum probability estimator developed by L. Weiss and J. Wolfowitz. The procedure given also generalizes C. Stein's fixed-width confidence sets to several dimensions.

Article information

Source
Ann. Statist., Volume 13, Number 2 (1985), 663-675.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176349546

Digital Object Identifier
doi:10.1214/aos/1176349546

Mathematical Reviews number (MathSciNet)
MR790564

Zentralblatt MATH identifier
0589.62067

JSTOR
links.jstor.org

Subjects
Primary: 62L12: Sequential estimation
Secondary: 62E20: Asymptotic distribution theory 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]

Keywords
Fixed-accuracy confidence set sequential methods nonlinear renewal theory general linear model maximum probability estimator

Citation

Finster, Mark. Estimation in the General Linear Model when the Accuracy is Specified Before Data Collection. Ann. Statist. 13 (1985), no. 2, 663--675. doi:10.1214/aos/1176349546. https://projecteuclid.org/euclid.aos/1176349546


Export citation