Sankhya: The Indian Journal of Statistics

2001, Volume 63, Series B, Pt. 3, pp. 338--350

A USEFUL STATISTIC FOR STUDYING OUTLIERS IN EXPERIMENTAL DESIGNS

By

LALMOHAN BHAR and V.K.GUPTA, Indian Agricultural Statistics Research Institute, New Delhi

SUMMARY. For testing outliers in the linear model (y, X(theta), (sigma)²I) for experimental designs, the Cook-statistic (Cook, 1977) is appropriately modified. Special emphasis is given to the case of a single outlier in block designs. This newly developed statistic is applied to a data set obtained from a randomized complete block design. A new cirterion for robustness of experimental designs against the presence of a single outlier is proposed. This new criterion is based on average Cook-statistic. A number of designs for one-way elimination of heterogeneity are identified that are robust against the presence of a single outlier.

AMS subject classification. 62K10.

Key words and phrases. Outlier, linear model, Cook-statistic, robustness.

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