The Annals of Statistics

Contrasts under Long-Range Correlations

H. Kunsch, J. Beran, and F. Hampel

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The background of the paper is the empirical observation from a variety of subject areas that long-range correlations appear to be much more frequent than has been previously assumed. This includes high-quality measurement series which are commonly treated as prototypes of "i.i.d." observations. Evidence is briefly cited in the paper. It has already been shown elsewhere that long-range dependence leads to results that can be qualitatively different from those obtained under short-range dependence, and in particular, that long-range dependence has drastic effects on the naive statistical treatment of absolute constants. The natural question arising from this, also of relevance for statistical practice, is how the long-range dependence affects the statistics for contrasts. The main answer given in this paper is twofold. (i) If the experimental conditions are well mixed as provided by randomization, the levels of tests and confidence intervals derived under the independence assumption are still correct, asymptotically and usually in good approximation for finite samples. (ii) Even under randomly mixed designs there are typically large unnoticed power and efficiency losses due to the long-range dependence. They can be greatly reduced without estimating the correlations by a simple blocking device.

Article information

Ann. Statist., Volume 21, Number 2 (1993), 943-964.

First available in Project Euclid: 12 April 2007

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Zentralblatt MATH identifier


Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 62F35: Robustness and adaptive procedures 62J10: Analysis of variance and covariance 62M99: None of the above, but in this section

Long-range dependence contrasts ordinary and generalized least squares regression with correlated errors robustness of validity robustness of efficiency randomization blocking


Kunsch, H.; Beran, J.; Hampel, F. Contrasts under Long-Range Correlations. Ann. Statist. 21 (1993), no. 2, 943--964. doi:10.1214/aos/1176349159.

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