Contrasts under long-range correlations

Künsch, Hans Rudolf; Beran, Jan; Hampel, Frank

Contrasts under long-range correlations

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Date

1993

Authors

Künsch, Hans Rudolf

Beran, Jan

Hampel, Frank

Publication type

Journal article

Published in

The Annals of Statistics ; 21 (1993), 2. - pp. 943-964

Abstract

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.

Subject (DDC)

510 Mathematics

Keywords

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

Cite This

ISO 690

KÜNSCH, Hans Rudolf, Jan BERAN, Frank HAMPEL, 1993. Contrasts under long-range correlations. In: The Annals of Statistics. 21(2), pp. 943-964. Available under: doi: 10.1214/aos/1176349159

BibTex

@article{Kunsch1993Contr-18818,
  year={1993},
  doi={10.1214/aos/1176349159},
  title={Contrasts under long-range correlations},
  number={2},
  volume={21},
  journal={The Annals of Statistics},
  pages={943--964},
  author={Künsch, Hans Rudolf and Beran, Jan and Hampel, Frank}
}

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