In 1936, H. Fairfield Smith (A discriminant function for plant selection, Annalsof Eugenice (London) 7,240-260) suggested a linear selection index for selecting varieties with higher genotypic values. Since then, the idea has been extended in various directions such as restricted selection indices. In this paper, linear selection indices are considered when, unlike squared error, the loss function is asymmetric. In particular, a LINEX loss function is considered for this purpose. It is shown that under multivariate normality, this approach still leads to the usual selection indices. Certain computational aspects are indicated.
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