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On the robustness of the linear hypothesis test procedure in the singular linear model with implied restrictions

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Abstract

The linear hypothesis test procedure is considered in the restricted linear modelsM r = {y, Xβ |Rβ = 0, σ 2V} andM *r = {y, Xβ |ARβ = 0, σ 2V}. Necessary and sufficient conditions are derived under which the statistic providing anF-test for the linear hypothesisH 0:Kβ=0 in the modelM *r (Mr) continues to be valid in the modelM r (M *r ); the results obtained cover the case whereM *r is replaced by the general Gauss-Markov modelM = {y, Xβ, σ 2V}.

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  1. Department of Mathematical and Statistical Methods, Agriculture University of Poznań, 60-637, Poznań, Poland

    P. R. Pordzik

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Pordzik, P.R. On the robustness of the linear hypothesis test procedure in the singular linear model with implied restrictions. Stat Papers 36, 69–75 (1995). https://doi.org/10.1007/BF02926020

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  • DOI: https://doi.org/10.1007/BF02926020

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