The Annals of Statistics

Robustness of Design Against Autocorrelation in Time I: Asymptotic Theory, Optimality for Location and Linear Regression

P. J. Bickel and Agnes M. Herzberg

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Abstract

A new asymptotic theory for studying the effect of dependence of the observations in experimental design for the linear model is developed. The uniform design is shown to be asymptotically optimal in a strong sense for estimating location and in a weaker sense for estimating the slope of a straight line regression. Numerical results supporting the asymptotics appear in a companion paper.

Article information

Source
Ann. Statist., Volume 7, Number 1 (1979), 77-95.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176344556

Digital Object Identifier
doi:10.1214/aos/1176344556

Mathematical Reviews number (MathSciNet)
MR515685

Zentralblatt MATH identifier
0403.62051

JSTOR
links.jstor.org

Keywords
6262 6215 6285 Experimental design autocorrelation in time optimal asymptotic

Citation

Bickel, P. J.; Herzberg, Agnes M. Robustness of Design Against Autocorrelation in Time I: Asymptotic Theory, Optimality for Location and Linear Regression. Ann. Statist. 7 (1979), no. 1, 77--95. doi:10.1214/aos/1176344556. https://projecteuclid.org/euclid.aos/1176344556


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See also

  • Part II: P. J. Bickel, Agnes M. Herzberg, M. F. Schilling. Robustness of Design Against Autocorrelation in Time, II: Optimality, Theoretical and Numerical Results for the First-Order Autoregressive Process. J. Amer. Statist. Assoc., vol. 76, no. 376, 870--877.