Joint one-sided tests of linear regression coefficients |
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| Affiliation: | 1. Institute of Space and Earth Information Science, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong;2. Shenzhen Research Institute, The Chinese University of Hong Kong, Shenzhen, China;3. Department of Geography and Resource Management, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong;1. Statistics School and Center of Statistical Research, Southwestern University of Finance and Economics, Chengdu, PR China;2. Department of Statistics and Probability, Michigan State University, East Lansing, MI 48823, United States;3. Department of Statistics and the Methodology Center, The Pennsylvania State University, University Park, PA 16802-2111, United States;4. Department of Business Statistics and Econometrics, Guanghua School of Management, Peking University, Beijing, 100871, PR China;5. Graduate School of Management, University of California, Davis, CA 95616-8609, United States;1. Institute of Cognitive Neuroscience, Department of Neuropsychology, Faculty of Psychology, Ruhr University Bochum, Universitätsstraße 150, 44780 Bochum, Germany;2. Institute for Experimental Psychology, Heinrich Heine University Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany |
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| Abstract: | The main example of the class of problems considered below is that of testing whether a subset of regression coefficients are jointly zero assuming knowledge of the coefficients' signs. If this knowledge is ignored, the likelihood ratio, Wald, and Lagrange multiplier tests are each equivalent to the F-test. We propose a new test which can be applied as a one-sided t-test and which is UMPI in a subspace of the parameter space. Empirical power comparisons with the power envelope, the F-test, and the exact one-sided likelihood ratio test show that the new test can have exceptionally good power over a wide range of the parameter space. |
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