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Abstract:
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Ranked set sampling is not well-suited for the design of experiments primarily for two reasons; it requires larger number of experimental units, and the role of randomization is not well defined. To resolve these concerns, recently order restricted randomized (ORR) designs have been developed and its properties have been discussed in the literature. In this paper, we develop nonparametric statistical inference for linear models in the context of order restricted randomized designs based on L1 norm. We derive the asymptotic distribution of the parameter estimates, and develop drop, Wald, and score tests for the contrast parameter. It is shown that ORR design performs better than its competitor in the literature. The Type I error is examined along with power comparisons. The properties of the estimators and tests are discussed under an arbitrary but consistent ranking scheme.
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