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SUMMARY Assuming a smooth trend plus independent error model for the environmental effects in the yields of a field plot experiment, least squares smoothing methods are developed to estimate both the treatment effects and the unknown trend. Treatment estimates are closely related to those resulting from a generalized least squares analysis in which the covariance structure for the environmental effects has a particular form. However, the main emphases are on the accuracy of treatment estimates under a fixed smooth trend plus error model and the exploratory power of the basic method to isolate trend effects of unknown form. Although the detailed development is for the one-dimensional case, generalizations of the smoothness concept and extensions to two dimensions are also discussed. Application of the basic method is illustrated on three data sets and the results compared with other analyses.
Green et al. (Tue,) studied this question.