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December, 1990 Accurate Multivariate Estimation Using Triple Sampling
Sharon L. Lohr
Ann. Statist. 18(4): 1615-1633 (December, 1990). DOI: 10.1214/aos/1176347869


Any multiresponse estimation experiment requires a decision about the number of observations to be taken. If the covariance is unknown, no fixed-sample-size procedure can guarantee that the joint confidence region will have an assigned shape and level. Double-sampling procedures use a preliminary sample of size $m$ to determine the minimum number of additional observations needed to achieve a prescribed accuracy and coverage probability for the parameter estimates. The triple-sampling procedures of this paper, less sensitive to the choice of $m$, revise the sample size estimate after collecting a fraction of the additional observations prescribed under double sampling. Second-order asymptotic results relying on conditional inference show that triple sampling is asymptotically consistent; in addition, the regret for triple sampling is a bounded function of the covariance structure and is independent of $m$.


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Sharon L. Lohr. "Accurate Multivariate Estimation Using Triple Sampling." Ann. Statist. 18 (4) 1615 - 1633, December, 1990.


Published: December, 1990
First available in Project Euclid: 12 April 2007

zbMATH: 0722.62041
MathSciNet: MR1074426
Digital Object Identifier: 10.1214/aos/1176347869

Primary: 62H12
Secondary: 62F25 , 62L12

Keywords: Confidence sets , multivariate normal distribution , sequential methods , Three-stage estimation

Rights: Copyright © 1990 Institute of Mathematical Statistics


Vol.18 • No. 4 • December, 1990
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