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Strange Design Points in Linear Regression
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 50 (2011) no. 2, pp. 103-110 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We discuss, partly on examples, several intuitively unexpected results in a standard linear regression model. We demonstrate that direct observations of the regression curve at a given point can not be substituted by observations at two very close neighboring points. On the opposite, we show that observations at two distant design points improve the variance of the estimator. In an experiment with correlated observations we show somewhat unexpected conditions under which a design point gives no or very little information about the estimated parameters, and so can be excluded from the design. For completeness we repeat briefly known conditions under which a design point is sensitive to the presence of outliers.
We discuss, partly on examples, several intuitively unexpected results in a standard linear regression model. We demonstrate that direct observations of the regression curve at a given point can not be substituted by observations at two very close neighboring points. On the opposite, we show that observations at two distant design points improve the variance of the estimator. In an experiment with correlated observations we show somewhat unexpected conditions under which a design point gives no or very little information about the estimated parameters, and so can be excluded from the design. For completeness we repeat briefly known conditions under which a design point is sensitive to the presence of outliers.
Classification : 62J05, 62K05
Keywords: singular models; optimal design; correlated observations 
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     title = {Strange {Design} {Points} in {Linear} {Regression}},
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Pázman, Andrej. Strange Design Points in Linear Regression. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 50 (2011) no. 2, pp. 103-110. http://geodesic.mathdoc.fr/item/AUPO_2011_50_2_a10/