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**Contrasts under long-range correlations.**
*(English)*
Zbl 0795.62077

The authors investigate the fact that most linear model procedures, which assume an i.i.d. error structure, seem to perform well even in the presence of long-range dependence amongst the errors. They find that the significance and confidence levels associated with constants are seriously affected but that those associated with contrasts are asymptotically correct under randomization of the treatments. In addition, for finite samples, they are approximately correct. Even with randomization, however, these statistical procedures may be very conservative, i.e. lack power or efficiency, in the presence of long- range dependence. This effect can be greatly reduced by using randomized block designs. The results of a small simulation experiment illustrate the findings.

Reviewer: E.McKenzie (Glasgow)

### MSC:

62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |

62J10 | Analysis of variance and covariance (ANOVA) |